---
id: 5900f4de1000cf542c50fff0
challengeType: 5
title: 'Problem 369: Badugi'
---

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler369()</code> should return 862400558448.
    testString: assert.strictEqual(euler369(), 862400558448, '<code>euler369()</code> should return 862400558448.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler369() {
  // Good luck!
  return true;
}

euler369();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
