# 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.