Watch the video or scroll down for the calculator.
The “Mathy” Way
When the order of items matters, that’s called a Permutation.
When the order of items doesn’t matter, that’s called a Combination. Since we are not allowed to repeat items, we use the following formula:
Number of possible Permutations
=
n^{r}
=
^{}
=
Number of possible Permutations
=
n!(n – r)!
=
!( – )!
=
Number of possible Combinations
=
(n + r – 1)!r!(n – 1)!
=
( + – 1)!!( – 1)!
=
Number of possible Combinations
=
n!r!(n – r)!
=
!!( – )!
=
The Visual Way
A form of the permutation problem that students commonly see is the “committee” problem. For example:
If there are 5 people, Jim, Jane, Bob, Susan, and Ralph, and only 3 of them can be on the new PTA committee, how many different combinations are possible?
In this example, there are 5 people to choose from (so n equals 5), and we need to choose 3 of them (so r equals 3).
Order doesn’t matter: if Jim is on the committee, he’s on the committee whether he’s picked first or last. Repetition isn’t allowed because Susan can’t be on the committee twice (even if she really wants to be!)
So, if we use the “mathy” way from above, we know the formula is:
Number of possible Combinations
=
n!r!(n – r)!
And we input the number 5 for n, and 3 for r, and so we know that there 10 possible combinations. But what does that actually mean?
Combinations Generator
I’ll show you using our generator:
All possible items:
No.
No.
Possibilities:
Permutation Calculator / Combination Calculator was last modified: October 31st, 2016 by Stephanie
71 thoughts on “Permutation Calculator / Combination Calculator”
Eric Craiger
This is so totally awesome!!! Helped me figure something out. Much thanks!!!
Frank
I am interested in how many choices a person would have to divide 36 months among 3 people?
Thanks!
Andale
Hi, Frank,
I’m not sure I understand your question completely but it might be the fundamental counting principle could help. 36 events (months), 3 ways to order each month so that’s 3^36.
If you can clarify a bit and post on our forum, one of our mods will be happy to help!
Stephanie
Frank
Here is the problem.
A person has 36 months to divide among 3 people.
How many different combinations could there be.
For example one combo would be 12 months each.
I like the calculator, however, my problem would need a slightly different formula that I haven’t found.
PROBLEM: I have 25 choices, and want to know the total number of combinations possible. Since I want combinations, not permutations, order does not matter. To keep it simple, repetition is not allowed. The combinations can be of any number of choices (r=1,2,3,…25). I can use the calculator and solve sequentially for r=1, r=2, r=3, etc., then sum the answers. However, there should be an equation that would solve the problem in one calculation. Can you show me that equation?
Thank you,
Art
Andale
Well, Art. The calculator uses the combinations formula (n!/(n-k!)k!). As you want to know k for all possible choices (1 to 25). I don’t know of a single equation other than a summation equation (Σ (n!/(n-k!)k! from n=1 to n=25)) I would suggest Excel. Copy the formula to 25 cells and then use autosum.
Art
OK, thanks. I appreciate the quick reply, and will probably use the spreadsheet method you suggested.
Art
Rachel G.
So if i have a 4-input combination lock that requires pink, green or purple as the input options. How many combinations are possible and can you list them? The order doesnt matter and they can be repeated. It would be really amazing if i could get this lock open! Ive been trying with no luck all weekend. Thanks in advance!
Ok so i have a lock that i need the combo to, i had it in third grade and the numbers are only 1-9 with the usual, only three in the combination. I need all the possible combos w/ repeating numbers hoping i can see the combo and remember and if not go through all the numbers manually.
matthew
Make that 0-9 numbers w/ 3 numbers in the combo.
Andale
Hello, Matthew,
Unfortunately I’m not not able to answer all stats question here on the site. Could you please post your question on our forums?
Al
Hello! I really like that the combinations generator physically shows all of the combinations. However, I need a slightly different calculator. I need to calculate and show all the combinations that 15 people can be in two groups (one of 7 and one of 8).
Andale
I don’t know of any calculators that will do that. If you find one, please let me know :)
Jefferson
This calculator works great because its assuming each N has the EXACT same number of R. What if some N have R=4 and some N have R=5?
Andale
In that case the combinations formula itself would chance, so you’d have to do two computations (the calculator is based on the combinations formula).
Andy
Thank you for your site. Could you tell me the formular for calculating possable combinations for 2 numbers and 2 letters Eg starting with 00AA
Thank you in advance for your help
Andy
Andale
Hello, Andy,
Could you please post this on our homework help forum? One of our moderators will be happy to help.
Regards,
Stephanie
Eda
JUST WHAT IVE BEEN LOOKIN FOR.
Thanks
AJ
If I have a 5 digit code,and the numbers can NOT be repeated how many codes can there be?
Andale
Hello, AJ,
Can you post on our homework help forum, please. One of our mods will be happy to help.
Robert williams
I have a locking device with 10 buttons which can all be pressed up to 3 times. The buttons can be pressed in any order, therefore the locking device is a combination lock. The user can set the code using any number of buttons from just one button to all the buttons.
I am trying to establish how many combinations they would be for this type of device.
Any help would be welcome.
Rob.
Andale
Hello, Robert,
Please post on our help forum:
One of our mods will be happy to help :)
Amit Gangaramani
Thanks a lot…
Amit Gangaramani
Thanks a lot
EUGENE JACK
i think that it;s fabulous that you came up with such an impressive way of calculating things,
loved it
Eric McCrea
I have a lock that consists of 5 numbers. Please help. The numbers are 56890. I need every different order to try and unlock it. Please help and thank you in advance.
Andale
Hi, Eric,
This needs the fundamental counting principle. You have 5 possible numbers, and each space on the lock has 5 possibilities so the answer is 5^5 (25) different ways.
Jacob
Can you please help me to find the right way to calculate this problem I have. I have 12 people in a group and in need to find the total number of possible pairs of 2. If what I have done is correct would it be 66?
Thanks in advance
Andale
Yes, it’s a permutation.
sherri
hi
i would like to find out how many different 12 digit combinations can you get using only numbers 1,2,3 and could you please list these different combinations for me.
Andale
Hi, Sherri,
Could you please post your question on our forum? One of our mods will be happy to help :)
Dwain
Is it possible for me to get a list of all five set combination from 1 and 22
eg 3,8,22,12,9
3,10,21,8,9
Oljeg
Hi, I am trying to find the solution (formula) for doing the following:
For any number of players (divisible by three), I need to calculate a number of rounds (in my case 8) for three players to play each other without any repetition.
So the first round of etc. 21 players would be:
1,2,3 4,5,6, 7,8,9 10,11,12 13,14,15 16,17,18 19,20, 21 and I am looking for the combinations for the next 7 rounds so that no one plays the same player again.
Regards,
Oljeg
Andale
Hi, Dwain,
Due to the volume of questions I get, I’m unable to answer every one. Could you post your question on the help forum? One of our mods will be happy to help. Thanks!
Andale
Hello, Oljeg,
Due to the volume of questions I get, I’m unable to answer every one. Could you post your question on the help forum? One of our mods will be happy to help. Thanks!
falco
hi,
I am amazed with your calculator, exactly what i needed, if i want to do the same calculator to excel, can you help me with the formula?
How would I calculate the different sets of 9 numbers with 3 numbers to a group, where no 2 numbers can be in the same group of 3 more than once?
An example set of 12 which works is 123, 456, 789, 147, 258, 369, 159, 267, 348, 168, 249, 357.
Andale
If I’m understanding your problem correctly, then you would just calculate combinations without repetition.
Apurva
Only one word. SUPER SUPER SUPER
jim neville
lhow many combinations of 6 numbers are there in 19 numbers – each number to feature only once in each combination?
Andale
I ran the calculator for n=19, r = 6 and got 27132.
Victor
Combinations & Permutation Calculator gives me the result of n=8, r =4 or 330 combinations. Is there an easy way to take those 330 combinations and separated them into groups by sum. For example show only combinations that add up 14, 15, 21, etc.
Andale
I would put them into an Excel spreadsheet and use the sort function to sort in ascending order. Then you can highlight by group…
Pius
Hello.. ..pls I want you to help me permutate 10 football teams to 2 event outcomes (that’s odd and even) goals
Andale
Hi, Pius,
I’m not sure exactly what you are asking. It’s possible to have (theoretically) an infinite amount of goals (1…infinity and 2…infinity) no matter how many teams you have. Could you please rephrase your question?
Dave
Hi,
I have a combination lock that I need all options for.
23-59-79 numbers in that order but each or all could be + or – 1 number. Can you help?
Thank you
Dave
Andale
I don’t know of a formula. I would write them out as there aren’t many, e.g 22 59 79, 23 59 79, 24 59 79…
Ryan
Hey I would like to know how many combinations there would be for a straight trifecta using 9 runners from the race, they are: Hartnell, Jameka, Oceanographer, HeartbreakCity, Almandin, BondiBeach, BigOrange, WicklowBrave, SecretNumber
Cheers
Steve
How many combinations are there with 5 numbers boxed
Andale
Hi, Steve,
What do you mean by “boxed”?
Andale
9! / (9 – 3)! = 504
Larry Burnette
I went in the hospital for surgery,went,wentinto a coma, and forgot my combination to my safe the three numbers i have 07-09-42# just need how many combinations and what they are for these three numbers. HELP
what is the possible combinations of the words over and under
Andale
Do you mean combinations of the letters in the words? Choosing all of them at the same time? Assuming the items do not repeat and that the order matters, that’s 362880 possibilities.
Kayemdee
Hi.
I have seven people to be on an out of hours duty roster. It needs to change every week on a repeating cycle. I need two people at any one time out of the pool of seven to be on call per week. How do I work out how they all do an equal amount of call duty and have as much time off as possible till they are back on call.
Andale
:
Scroll down to Combinations Generator. If you input the names, it will give you the list of possibilities. Then just group the results manually to address max time between calls.
Kayemdee
Thank you for the perms.
Knight
I have 17 numbers and want to select 5 numbers from them, how to I get the all the combination to this please and permutations please many thanks
1 4 8 10 13 17 19 22 26 28 31 35 37 40 44 46 49
Knight
Forgot one number 53
Andale
Knight,
Just type them into the combinations generator (scroll down the page).
JacqK
You want to form a 5 letter code word using the letters A, B, C, D, E and numbers
1, 2, 3, 4, 5 and allowing for repetition of letters and numbers.
(a) How many different code words can you form?
(b) What is the probability that a letter or a number is repeated?
(c) What is the probability that no number is repeated?
Andale
Hi, Jacq,
You can use the calculator to answer (a).
For b and c, use the combinations generator (scroll down). Find your outputs and from there you should be able to figure out the probabilities.
Rose
I am looking for all of the possible 5 and also 6 letter words that can come from the letters, C, C, H, O, R, U, S.
They may be in ANY order. This would have all words beginning with C through S. The calculator only shows words beginning with the 1st C. Since there are 2 C’s, then a word may contain 2 C’s, but not all words will have 2 C’s.
How can I find the correct word combinations?
Andale
Rose, I typed in C,C,H,O,R,U,S into the generator at the bottom and it did come up with a list that included two CCs. That said, it isn’t going to give you words — the letters will still be scrambled.
C, C, H, O, R
C, C, H, O, U
C, C, H, O, S
C, C, H, R, U
C, C, H, R, S
C, C, H, U, S
C, C, O, R, U
C, C, O, R, S
C, C, O, U, S
C, C, R, U, S
C, H, O, R, U
C, H, O, R, S
C, H, O, U, S
C, H, R, U, S
C, O, R, U, S
C, H, O, R, U
C, H, O, R, S
C, H, O, U, S
C, H, R, U, S
C, O, R, U, S
H, O, R, U, S
Rose
That is okay, since you can use any of the set letters to make a word. The letters may be in any order.
When using the letters C,C,H,O,R,U,S, they may be as such:
CHORUS
OCCURS
There is nothing saying the letters must be in the same order.
Thank you for your help.
This is so totally awesome!!! Helped me figure something out. Much thanks!!!
I am interested in how many choices a person would have to divide 36 months among 3 people?
Thanks!
Hi, Frank,
I’m not sure I understand your question completely but it might be the fundamental counting principle could help. 36 events (months), 3 ways to order each month so that’s 3^36.
If you can clarify a bit and post on our forum, one of our mods will be happy to help!
Stephanie
Here is the problem.
A person has 36 months to divide among 3 people.
How many different combinations could there be.
For example one combo would be 12 months each.
You can still use the fundamental counting principle.
I like the calculator, however, my problem would need a slightly different formula that I haven’t found.
PROBLEM: I have 25 choices, and want to know the total number of combinations possible. Since I want combinations, not permutations, order does not matter. To keep it simple, repetition is not allowed. The combinations can be of any number of choices (r=1,2,3,…25). I can use the calculator and solve sequentially for r=1, r=2, r=3, etc., then sum the answers. However, there should be an equation that would solve the problem in one calculation. Can you show me that equation?
Thank you,
Art
Well, Art. The calculator uses the combinations formula (n!/(n-k!)k!). As you want to know k for all possible choices (1 to 25). I don’t know of a single equation other than a summation equation (Σ (n!/(n-k!)k! from n=1 to n=25)) I would suggest Excel. Copy the formula to 25 cells and then use autosum.
OK, thanks. I appreciate the quick reply, and will probably use the spreadsheet method you suggested.
Art
So if i have a 4-input combination lock that requires pink, green or purple as the input options. How many combinations are possible and can you list them? The order doesnt matter and they can be repeated. It would be really amazing if i could get this lock open! Ive been trying with no luck all weekend. Thanks in advance!
81
{pink,pink,pink,pink} {pink,pink,pink,green} {pink,pink,pink,purple} {pink,pink,green,pink} {pink,pink,green,green} {pink,pink,green,purple} {pink,pink,purple,pink} {pink,pink,purple,green} {pink,pink,purple,purple} {pink,green,pink,pink} {pink,green,pink,green} {pink,green,pink,purple} {pink,green,green,pink} {pink,green,green,green} {pink,green,green,purple} {pink,green,purple,pink} {pink,green,purple,green} {pink,green,purple,purple} {pink,purple,pink,pink} {pink,purple,pink,green} {pink,purple,pink,purple} {pink,purple,green,pink} {pink,purple,green,green} {pink,purple,green,purple} {pink,purple,purple,pink} {pink,purple,purple,green} {pink,purple,purple,purple} {green,pink,pink,pink} {green,pink,pink,green} {green,pink,pink,purple} {green,pink,green,pink} {green,pink,green,green} {green,pink,green,purple} {green,pink,purple,pink} {green,pink,purple,green} {green,pink,purple,purple} {green,green,pink,pink} {green,green,pink,green} {green,green,pink,purple} {green,green,green,pink} {green,green,green,green} {green,green,green,purple} {green,green,purple,pink} {green,green,purple,green} {green,green,purple,purple} {green,purple,pink,pink} {green,purple,pink,green} {green,purple,pink,purple} {green,purple,green,pink} {green,purple,green,green} {green,purple,green,purple} {green,purple,purple,pink} {green,purple,purple,green} {green,purple,purple,purple} {purple,pink,pink,pink} {purple,pink,pink,green} {purple,pink,pink,purple} {purple,pink,green,pink} {purple,pink,green,green} {purple,pink,green,purple} {purple,pink,purple,pink} {purple,pink,purple,green} {purple,pink,purple,purple} {purple,green,pink,pink} {purple,green,pink,green} {purple,green,pink,purple} {purple,green,green,pink} {purple,green,green,green} {purple,green,green,purple} {purple,green,purple,pink} {purple,green,purple,green} {purple,green,purple,purple} {purple,purple,pink,pink} {purple,purple,pink,green} {purple,purple,pink,purple} {purple,purple,green,pink} {purple,purple,green,green} {purple,purple,green,purple} {purple,purple,purple,pink} {purple,purple,purple,green} {purple,purple,purple,purple}
Ok so i have a lock that i need the combo to, i had it in third grade and the numbers are only 1-9 with the usual, only three in the combination. I need all the possible combos w/ repeating numbers hoping i can see the combo and remember and if not go through all the numbers manually.
Make that 0-9 numbers w/ 3 numbers in the combo.
Hello, Matthew,
Unfortunately I’m not not able to answer all stats question here on the site. Could you please post your question on our forums?
Hello! I really like that the combinations generator physically shows all of the combinations. However, I need a slightly different calculator. I need to calculate and show all the combinations that 15 people can be in two groups (one of 7 and one of 8).
I don’t know of any calculators that will do that. If you find one, please let me know :)
This calculator works great because its assuming each N has the EXACT same number of R. What if some N have R=4 and some N have R=5?
In that case the combinations formula itself would chance, so you’d have to do two computations (the calculator is based on the combinations formula).
Thank you for your site. Could you tell me the formular for calculating possable combinations for 2 numbers and 2 letters Eg starting with 00AA
Thank you in advance for your help
Andy
Hello, Andy,
Could you please post this on our homework help forum? One of our moderators will be happy to help.
Regards,
Stephanie
JUST WHAT IVE BEEN LOOKIN FOR.
Thanks
If I have a 5 digit code,and the numbers can NOT be repeated how many codes can there be?
Hello, AJ,
Can you post on our homework help forum, please. One of our mods will be happy to help.
I have a locking device with 10 buttons which can all be pressed up to 3 times. The buttons can be pressed in any order, therefore the locking device is a combination lock. The user can set the code using any number of buttons from just one button to all the buttons.
I am trying to establish how many combinations they would be for this type of device.
Any help would be welcome.
Rob.
Hello, Robert,
Please post on our help forum:
One of our mods will be happy to help :)
Thanks a lot…
Thanks a lot
i think that it;s fabulous that you came up with such an impressive way of calculating things,
loved it
I have a lock that consists of 5 numbers. Please help. The numbers are 56890. I need every different order to try and unlock it. Please help and thank you in advance.
Hi, Eric,
This needs the fundamental counting principle. You have 5 possible numbers, and each space on the lock has 5 possibilities so the answer is 5^5 (25) different ways.
Can you please help me to find the right way to calculate this problem I have. I have 12 people in a group and in need to find the total number of possible pairs of 2. If what I have done is correct would it be 66?
Thanks in advance
Yes, it’s a permutation.
hi
i would like to find out how many different 12 digit combinations can you get using only numbers 1,2,3 and could you please list these different combinations for me.
Hi, Sherri,
Could you please post your question on our forum? One of our mods will be happy to help :)
Is it possible for me to get a list of all five set combination from 1 and 22
eg 3,8,22,12,9
3,10,21,8,9
Hi, I am trying to find the solution (formula) for doing the following:
For any number of players (divisible by three), I need to calculate a number of rounds (in my case 8) for three players to play each other without any repetition.
So the first round of etc. 21 players would be:
1,2,3 4,5,6, 7,8,9 10,11,12 13,14,15 16,17,18 19,20, 21 and I am looking for the combinations for the next 7 rounds so that no one plays the same player again.
Regards,
Oljeg
Hi, Dwain,
Due to the volume of questions I get, I’m unable to answer every one. Could you post your question on the help forum? One of our mods will be happy to help. Thanks!
Hello, Oljeg,
Due to the volume of questions I get, I’m unable to answer every one. Could you post your question on the help forum? One of our mods will be happy to help. Thanks!
hi,
I am amazed with your calculator, exactly what i needed, if i want to do the same calculator to excel, can you help me with the formula?
Falco,
You can find the Excel formulas here.
I just want combinations of any four numbers out of ten
That would be 5040 possible combinations, assuming the order doesn’t matter.
How would I calculate the different sets of 9 numbers with 3 numbers to a group, where no 2 numbers can be in the same group of 3 more than once?
An example set of 12 which works is 123, 456, 789, 147, 258, 369, 159, 267, 348, 168, 249, 357.
If I’m understanding your problem correctly, then you would just calculate combinations without repetition.
Only one word. SUPER SUPER SUPER
lhow many combinations of 6 numbers are there in 19 numbers – each number to feature only once in each combination?
I ran the calculator for n=19, r = 6 and got 27132.
Combinations & Permutation Calculator gives me the result of n=8, r =4 or 330 combinations. Is there an easy way to take those 330 combinations and separated them into groups by sum. For example show only combinations that add up 14, 15, 21, etc.
I would put them into an Excel spreadsheet and use the sort function to sort in ascending order. Then you can highlight by group…
Hello.. ..pls I want you to help me permutate 10 football teams to 2 event outcomes (that’s odd and even) goals
Hi, Pius,
I’m not sure exactly what you are asking. It’s possible to have (theoretically) an infinite amount of goals (1…infinity and 2…infinity) no matter how many teams you have. Could you please rephrase your question?
Hi,
I have a combination lock that I need all options for.
23-59-79 numbers in that order but each or all could be + or – 1 number. Can you help?
Thank you
Dave
I don’t know of a formula. I would write them out as there aren’t many, e.g 22 59 79, 23 59 79, 24 59 79…
Hey I would like to know how many combinations there would be for a straight trifecta using 9 runners from the race, they are: Hartnell, Jameka, Oceanographer, HeartbreakCity, Almandin, BondiBeach, BigOrange, WicklowBrave, SecretNumber
Cheers
How many combinations are there with 5 numbers boxed
Hi, Steve,
What do you mean by “boxed”?
9! / (9 – 3)! = 504
I went in the hospital for surgery,went,wentinto a coma, and forgot my combination to my safe the three numbers i have 07-09-42# just need how many combinations and what they are for these three numbers. HELP
6 possibilities
7 9 42
7 42 9
9 7 42
9 42 7
42 7 9
42 9 7
what is the possible combinations of the words over and under
Do you mean combinations of the letters in the words? Choosing all of them at the same time? Assuming the items do not repeat and that the order matters, that’s 362880 possibilities.
Hi.
I have seven people to be on an out of hours duty roster. It needs to change every week on a repeating cycle. I need two people at any one time out of the pool of seven to be on call per week. How do I work out how they all do an equal amount of call duty and have as much time off as possible till they are back on call.
:
Scroll down to Combinations Generator. If you input the names, it will give you the list of possibilities. Then just group the results manually to address max time between calls.
Thank you for the perms.
I have 17 numbers and want to select 5 numbers from them, how to I get the all the combination to this please and permutations please many thanks
1 4 8 10 13 17 19 22 26 28 31 35 37 40 44 46 49
Forgot one number 53
Knight,
Just type them into the combinations generator (scroll down the page).
You want to form a 5 letter code word using the letters A, B, C, D, E and numbers
1, 2, 3, 4, 5 and allowing for repetition of letters and numbers.
(a) How many different code words can you form?
(b) What is the probability that a letter or a number is repeated?
(c) What is the probability that no number is repeated?
Hi, Jacq,
You can use the calculator to answer (a).
For b and c, use the combinations generator (scroll down). Find your outputs and from there you should be able to figure out the probabilities.
I am looking for all of the possible 5 and also 6 letter words that can come from the letters, C, C, H, O, R, U, S.
They may be in ANY order. This would have all words beginning with C through S. The calculator only shows words beginning with the 1st C. Since there are 2 C’s, then a word may contain 2 C’s, but not all words will have 2 C’s.
How can I find the correct word combinations?
Rose, I typed in C,C,H,O,R,U,S into the generator at the bottom and it did come up with a list that included two CCs. That said, it isn’t going to give you words — the letters will still be scrambled.
C, C, H, O, R
C, C, H, O, U
C, C, H, O, S
C, C, H, R, U
C, C, H, R, S
C, C, H, U, S
C, C, O, R, U
C, C, O, R, S
C, C, O, U, S
C, C, R, U, S
C, H, O, R, U
C, H, O, R, S
C, H, O, U, S
C, H, R, U, S
C, O, R, U, S
C, H, O, R, U
C, H, O, R, S
C, H, O, U, S
C, H, R, U, S
C, O, R, U, S
H, O, R, U, S
That is okay, since you can use any of the set letters to make a word. The letters may be in any order.
When using the letters C,C,H,O,R,U,S, they may be as such:
CHORUS
OCCURS
There is nothing saying the letters must be in the same order.
Thank you for your help.