Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

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 + 1)! ways. Therefore, the probability for the required event is $\frac{(n-k+1)!}{n!}$.