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March 29, 2017

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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 - ,

    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

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