[jeokbovb] Binomial 52

Choosing k cards randomly from a deck of size n=52 is a common operation.  Elegant values of k are the factors of 52.

For example, we imagine arranging the 52 shuffled cards in a rectangle face down and flipping over one row or column (or something like that: one card per row, etc.).

52 choose 2 = 1326
52 choose 4 = 270725
52 choose 13 = 635013559600 ~= 6e11
52 choose 26 = 495918532948104 ~= 5e14

Or half the deck:

26 choose 2 = 325
26 choose 13 = 10400600 ~= 1e7

Permutations would be larger by a factor of k!.

Perhaps we care about multinomials, for example, dividing the 52 cards into 4 piles of 13 (as done in bridge).

If we include the 2 jokers, 54 has richer possibilities of rectangle shapes: widths 2, 3, 6, 9, 18, 27.  A 48-card deck, 12 cards per suit, also has lots of divisors.

Previously, 12 choose 6.