---
id: 5900f45c1000cf542c50ff6e
challengeType: 5
title: 'Problem 239: Twenty-two Foolish Primes'
forumTopicId: 301884
---
## Description
A set of disks numbered 1 through 100 are placed in a line in random order.
What is the probability that we have a partial derangement such that exactly 22 prime number discs are found away from their natural positions?
(Any number of non-prime disks may also be found in or out of their natural positions.)
Give your answer rounded to 12 places behind the decimal point in the form 0.abcdefghijkl.
## Instructions
## Tests
```yml
tests:
- text: euler239() should return 0.001887854841.
testString: assert.strictEqual(euler239(), 0.001887854841);
```
## Challenge Seed
```js
function euler239() {
return true;
}
euler239();
```