---
id: 5900f4de1000cf542c50fff0
challengeType: 5
title: 'Problem 369: Badugi'
---
## Description
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.
## Instructions
## Tests
```yml
tests:
- text: euler369() should return 862400558448.
testString: assert.strictEqual(euler369(), 862400558448, 'euler369() should return 862400558448.');
```
## Challenge Seed
```js
function euler369() {
// Good luck!
return true;
}
euler369();
```