## Badugi

### Problem 369

Published on Sunday, 29th January 2012, 04:00 am; Solved by 293In 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.