Question

Three married couples go to a movie theater. if they sit together in a row of 6 empty seats, find the probability that each woman is to the left of her husband.

Answer 1

Given are three married couples.

So, let us assume there are 3 men and 3 women

They are sitting in a row of 6 empty seats

There is a definite order constraint that each woman will sit left to her husband. The first woman gets 3 options to choose from 3 available seats. The second woman has two options left as already one seat is filled by the first woman. The last woman has one option left. So, it is $3*2*1$

So, number of ways is 3! = $3*2*1$ = 6 ways.