题目239：22个错位的素数

欧拉计划

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.

题目：

一个编号为 1 到 100 的圆盘集合随机排成一条直线。

其中正好有 22 个素数圆盘发生错位不在其自然位置上的可能性为多少？
(任何非素数圆盘也可能不在其自然位置上)

给出你的答案并精确到 12 位小数，形式为 0.abcdefghijkl 。