Question

In how many ways can 10 boys be seated in a row having 28 seats such that no two friends occupy adjacent seats?

(a) ^13P5

(b) ^9P29

(c) ^19P10

(d) ^15P7

This question was addressed to me in an interview.

This intriguing question originated from Counting topic in portion Counting of Discrete Mathematics

Answer 1

Correct choice is (c) ^19P10

Easy explanation: First let us take the 18 unoccupied seats. They create 19 slots i.e., one on the left of each seat and one on the right of the last one. So we can place the 10 boys in any of these 19 slots that are, ^19P10 ways.