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?
+128475 The total possible arrangements are 9! = 362800 arrangements
If we count the ones where NO women stand next to each other ....then note that the women can occupy
positions 1 - 3 - 5 -7 or 2 - 4 -6 - 8 or 3 - 5 -7 - 9 = 3 ways
And for each of these the women can be arranged in 4! = 24 ways
And for each of these the men can be arranged in 5! =120 ways
So....the number of arrangements where at least two of the women stand to each other =
9! - (3) (24)(120) =
362800 - 8640 =
354,240 possible arrangements
