Suppose n objects are permuted at random among themselves wh

Suppose n objects are permuted at random among themselves, what is the probability that k specified objects occupy k specified objects? (Each of k specified objects occupies a specified position)

Solution

So here, there are n! ways to permut the n objects.

If you fix k objects, then you can only permut n - k objects. Doing so, you have (n - k)! ways.

Thus, the probability that k objects already assume a specific position is

Probability = (n - k)! / n! [ANSWER]