Posted by Jason on .
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?

Discrete Math 
MathMate,
Take out Ed and Gail (7 people left). Choose 5 at a time to take pictures without the couple. There are
N1=7!/(72)! 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