# 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.