Posted by Jason on Thursday, October 27, 2011 at 6:08pm.
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, Thursday, October 27, 2011 at 9:15pm
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
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