Four couples have reserved seats in a row for a concert. In how many different ways can they be seated if

(a) there are no seating restrictions?

(b) the two members of each couple wish to sit together?

a) 40320 ways

b) 384 ways

Step-by-step explanation:

a) if there are no seating restrictions, the number of ways the 4 couples can be seated is the permutation of 8 persons in 8 seats then

number of ways = permutation of 8 persons in 8 seats = 8! = 40320

b) if each couple will sit together then the number of ways is:

number of ways = number of permutation of 4 integrants of each couple in 4 pairs of seats * number of permutation for a couple in a pair of seats^ number of pair of seats = 4! * 2^4 = 384