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 no couple is to be separated?

Answer 1

given four married couples and no couples to be separated. so if name the seats as 1,2,3,4,5,6,7,8 and starting with 1 then anyone among the 8 persons can seat at seat 1 and spouse of the person can seat besides him/her on seat 2. similarly on seat 3 among rest 6 any one can seat and on seat 4 spouse of the person can seat. on seat no 5 anyone among 4 can seat and on seat 6 and spouse seat on 6. on seat 7 anyone among 2 can seat and on seat 8 spouse will seat.

so 1=8,2=1,3=6,4=1,5=4,6=1,7=2,8=1

total ways= 8*1*6*1*4*1*2*1= 384