Four married couples are to be seated in a row having 8 chairs. The number of ways so that spouses are seated next to each other, is

Question

Four married couples are to be seated in a row having 8 chairs. The number of ways so that spouses are seated next to each other, is (A) 72 (B) 186 (C) 384 (D) 516

Tardigrade Admin · Accepted Answer

Let us denote the four married couples of

C_{1}

,

C_{2}, C_{3}

and

C_{4}

. We consider each couple as one unit. We can permute four units in 4 ! ways. Each couple can be seated in 2 ! ways. Thus, the required number of ways is

(4!) (2) (2) (2) (2) = 384

.

Q. Four married couples are to be seated in a row having 8 chairs. The number of ways so that spouses are seated next to each other, is

72

186

384

516

Let us denote the four married couples of C1​, C2​,C3​ and C4​. We consider each couple as one unit. We can permute four units in 4 ! ways. Each couple can be seated in 2 ! ways. Thus, the required number of ways is (4!)(2)(2)(2)(2)=384.

Let us denote the four married couples of $C_{1}$ , $C_{2}, C_{3}$ and $C_{4}$ . We consider each couple as one unit. We can permute four units in 4 ! ways. Each couple can be seated in 2 ! ways. Thus, the required number of ways is
$(4!) (2) (2) (2) (2) = 384$ .