---
id: 5900f4fa1000cf542c51000d
challengeType: 5
title: '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.
## Instructions
## Tests
```yml
tests:
- text: euler398() should return 2010.59096.
testString: assert.strictEqual(euler398(), 2010.59096, 'euler398() should return 2010.59096.');
```
## Challenge Seed
```js
function euler398() {
// Good luck!
return true;
}
euler398();
```