---
id: 5900f45c1000cf542c50ff6e
title: 'Problem 239: Twenty-two Foolish Primes'
challengeType: 1
forumTopicId: 301884
dashedName: problem-239-twenty-two-foolish-primes
---

# --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.

# --hints--

`twentyTwoFoolishPrimes()` should return `0.001887854841`.

```js
assert.strictEqual(twentyTwoFoolishPrimes(), 0.001887854841);
```

# --seed--

## --seed-contents--

```js
function twentyTwoFoolishPrimes() {

  return true;
}

twentyTwoFoolishPrimes();
```

# --solutions--

```js
// solution required
```
