Problem 239

Twenty-two Foolish Primes

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.

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**