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A committee has five women and four men. (All the committee members are distinguishable.) How many ways can they stand in a row for a photograph, so that at least two of the women are standing next to each other?

 Dec 21, 2019
 #1
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First, we choose the two women to stand next to each other.  We can do this in 5*4/2 = 10 ways.  There are then 8 ways to choose the two places where they stand next to each other.  There are 7 other people on the committee, so there are 10*8*7! ways to arrange the members.  Answer = 403200.

 Dec 21, 2019
 #3
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Thanks!  403,200 was correct.

Guest Dec 23, 2019
 #2
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9! - [5! * 4!] =360,000 ways.

 Dec 21, 2019

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