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:
19 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
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