Question

Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if there are no restrictions on the seating arrangement? Group of answer choicesa. with no restrictions?b. if each couple is to sit together?c. if all men sit together to the right of all women?

Answer 1

Answer:

a. 40,320

b. 384

c. 576

Step-by-step explanation:

a. If there are no restrictions, the number of arrangements is given by a permutation of 8 people in 8 spots:

$n=\frac{8!}{(8-8)!}= 40,320\ ways$

b. if each couple is to sit together,  the number of arrangements is given by a permutation of 4 couples in 4 spots multiplied by 2⁴ (representing the men and women from each couple switching places):

$n=\frac{4!}{(4-4)!}*2^4= 384\ ways$

c. if all men sit together to the right of all women, the number of arrangements is given by a permutation of 4 men in 4 spots multiplied by a permutation of 4 women in 4 spots:

$n=\frac{4!}{(4-4)!}*\frac{4!}{(4-4)!}=576\ ways$