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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?

 Feb 10, 2020
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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

 

 

cool cool cool

 Feb 10, 2020
edited by CPhill  Feb 10, 2020

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