Problem 369

Problem 369


In a standard 52 card deck of playing cards, a set of 4 cards is a Badugi if it contains 4 cards with no pairs and no two cards of the same suit.

Let f(n) be the number of ways to choose n cards with a 4 card subset that is a Badugi. For example, there are 2598960 ways to choose five cards from a standard 52 card deck, of which 514800 contain a 4 card subset that is a Badugi, so f(5) = 514800.

Find ∑f(n) for 4 ≤ n ≤ 13.



记f(n)为选择n张牌,使得其中有4张牌构成百得之的方法数。例如,从一副标准扑克牌的52张非鬼牌中取出5张,一共有2598960种取法,其中有514800种包含4张牌构成百得之,因此f(5) = 514800。

对于4 ≤ n ≤ 13,求∑f(n)。