data/problems/369.yml
---
:id: 369
:name: Badugi
:url: https://projecteuler.net/problem=369
:content: |+
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(<var>n</var>) be the number of ways to choose <var>n</var> 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(<var>n</var>) for 4 ≤ <var>n</var> ≤ 13.