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.
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