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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)!
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:
5252598960Number of 5 card hands in a deck of 52 cards
527133784560Number of 7 card hands in a deck of 52 cards
5213635013559600Number of 7 card hands in a deck of 52 cards
52521Number 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);

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


In reply to Golf: Selection from sets (Choose) by knobunc

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