Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Wakiki Beach Resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith(as he says they are always together otherwise), how many ways the group can be arranged in a row for the photograph?
a.20! b.19!+18! c. 18*19! d.2*19!
and my answer is c
is it correct

Question

Mr and Mrs Smith have invited 9 of their friends and their spouses for a party at the Wakiki Beach Resort. They stand for a group photograph. If Mr Smith never stands next to Mrs Smith(as he says they are always together otherwise), how many ways the group can be arranged in a row for the photograph?
a.20!      b.19!+18!                    c. 18*19!                      d.2*19!
and my answer is c 
is it correct

kropot72 · Answer

There are 18! possible permutations of the guests. Mr Smith can be placed in 19 possible positions in each of the 18! permutations of guests and Mrs Smith can be placed in 18 possible positions for each placement of Mr Smith without standing next to him. Therefore there are 19 * 18 possible permutations of Mr and Mrs Smith, each of which can be taken with each of the 18! permutations of guests.
The group can be arranged in 19 * 18 * 18! = 18 * 19! ways.
Your choice of c is correct. Good work!