The numbers 1,2,3, ..., n are arrange in a random order. The probability that the digits 1, 2, 3, . . ., k (k < n) appear as neighbors in that order is

The number of ways of arranging n numbers is n! In each order obtained, we must now arrange the digits 1, 2, ..., k as group and the n - k remaining digits. This can be done in (n - k + l)! ways. Therefore, the probability for the required event isn-k+1!n!