---
id: 5900f4de1000cf542c50fff0
title: 'Problem 369: Badugi'
challengeType: 5
forumTopicId: 302030
dashedName: 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.

# --hints--

`euler369()` should return 862400558448.

```js
assert.strictEqual(euler369(), 862400558448);
```

# --seed--

## --seed-contents--

```js
function euler369() {

  return true;
}

euler369();
```

# --solutions--

```js
// solution required
```