Ordinal probability question

dr6

New Member
#1
Person A and Person B both get the integers 1, 2 ... N. They independently arrange them in to truly random order.

The compare their first digits to see if they are the same, and then their second numbers and so on.

What is the probability that x of their digits are the same? Well, for X = N, the answer is 1/N!. For X = N-1, the answer is 0. But what about for other X? Is a nice formula available?