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

# --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.

# --hints--

`euler398()` should return 2010.59096.

```js
assert.strictEqual(euler398(), 2010.59096);
```

# --seed--

## --seed-contents--

```js
function euler398() {

  return true;
}

euler398();
```

# --solutions--

```js
// solution required
```