In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?

Answer: Option A

First let us consider the 28 unoccupied seats.
They create 29 slots - one on the left of each seat and one on the right of the last one.
We can place the 7 friends in any of these 29 slots i.e. ²⁹P₇ ways.