Golf: Selection from sets (Choose)

Since there was just a golf for factorials, I figured that doing one for the number of ways to select M objects from a set of N objects without repetition might be appropriate.

Basically, if I have a set of 4 cards, how many ways can I select a hand of 1 card from the set without repeating myself? The answer is obviously 4. Now if I have a hand size of 2 how many ways are there? The answer is 6, but it is less obvious.

The general solution is defined by the function:

Choose(M, N) =        M!
               ----------------
                N! * (M - N)!
[download]

Where M is the size of the set and N is the number of cards to select. And M! is the factorial of M. See Golf: Factorials for more info.

The following are test cases that you can use:

M N Answer Notes

52 5 2598960 Number of 5 card hands in a deck of 52 cards

52 7 133784560 Number of 7 card hands in a deck of 52 cards

52 13 635013559600 Number of 7 card hands in a deck of 52 cards

52 52 1 Number of ways to select a hand size of 1 from a 52 card deck

M	N	Answer	Notes
52	5	2598960	Number of 5 card hands in a deck of 52 cards
52	7	133784560	Number of 7 card hands in a deck of 52 cards
52	13	635013559600	Number of 7 card hands in a deck of 52 cards
52	52	1	Number of ways to select a hand size of 1 from a 52 card deck

The interface for the resulting code should be:

print c($m, $n);
[download]

If you want to define a factorial subroutine that should be included in the size of the code.

-ben

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