Of the nine (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal and Ida), five of them stand in a row for a picture, how many ways can this be done if Ed and Gail are standing next to each other in the picture?

Answer 1

Take out Ed and Gail (7 people left). Choose 5 at a time to take pictures without the couple. There are
N1=7!/(7-2)! possible pictures.

Now treat the couple as a single person, and get 3 other people for pictures (N2).
Don't forget to ask Gail and Ed to change places (2*N2)

Add up the two to get the total=N1+2N2