Question

Four married couples have reserved eight seats in a row at the theater. If they arrange themselves​ randomly, what is the probability that all the women will sit in adjacent seats and all the men will sit in adjacent​ seats?

Answer 1

The required probability is 2.86%.

Step-by-step explanation:

The number of ways in which eight persons can sit within themselves at the reserved eight seats is given by

`N=8!.`

And, the number of ways in which 4 couples (8 persons) can sit such that all the women will sit in adjacent seats and all the men will sit in adjacent​ seats is given by

`n=4!*4!*2!.`

Therefore, the probability that all the women will sit in adjacent seats and all the men will sit in adjacent​ seats is

`p=(n)/(N)=(4!*4!*2!)/(8!)=(4*3*2*1*4!*2*1)/(8*7*6*5*4!)=(1)/(35)=2.86\%.`

Thus, the required probability is 2.86%.