Question

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?

Answer 1

a) 40320 ways

b) 384 ways

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