---

Problem 369

---

Badugi

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.

---

百得之

从一副标准扑克牌的52张非鬼牌中取出4张，如果其中没有两张牌点数相同或花色相同，则称为百得之。

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)。

---