SOLUTION: In how many ways can 6 men and 4 women sit in a row if the men must sit together and the women must sit together. I thought it was 6!4! = 17280 possible arrangements but now I a

Algebra ->  Permutations -> SOLUTION: In how many ways can 6 men and 4 women sit in a row if the men must sit together and the women must sit together. I thought it was 6!4! = 17280 possible arrangements but now I a      Log On


   

Question 514874: In how many ways can 6 men and 4 women sit in a row if the men must sit together and the women must sit together.
I thought it was 6!4! = 17280 possible arrangements but now I am second guessing.
Thanks for your help!
Answer by drcole(72) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct that there are 6! = 720 ways that we could arrange six men in a row, and 4! = 24 ways to arrange four women in a row, but since all of the men and all of the women need to sit together, we also have to take into account how the two groups are arranged:
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So there are actually 6!4!2 = (720)(24)(2) = 34,560 ways to rearrange the six men and four women as specified.