Statistics How To

Permutation Calculator / Combination 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  
=    nr
 
=   
 
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:



5 thoughts on “Permutation Calculator / Combination Calculator

  1. Frank

    I am interested in how many choices a person would have to divide 36 months among 3 people?
    Thanks!

  2. 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

  3. 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.

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