---
id: 5900f4fa1000cf542c51000d
challengeType: 5
title: 'Problem 398: Cutting rope'
forumTopicId: 302063
---

## Description
<section id='description'>
Inside a rope of length n, n-1 points are placed with distance 1 from each other and from the endpoints. Among these points, we choose m-1 points at random and cut the rope at these points to create m segments.


Let E(n, m) be the expected length of the second-shortest segment.
For example, E(3, 2) = 2 and E(8, 3) = 16/7.
Note that if multiple segments have the same shortest length the length of the second-shortest segment is defined as the same as the shortest length.


Find E(107, 100).
Give your answer rounded to 5 decimal places behind the decimal point.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler398()</code> should return 2010.59096.
    testString: assert.strictEqual(euler398(), 2010.59096);

```

</section>

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

<div id='js-seed'>

```js
function euler398() {
  // Good luck!
  return true;
}

euler398();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>