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Math Help - A question which my friend gave me

  1. #1
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    A question which my friend gave me

    6 men and 3 women stand in a Straight line
    How many diff ways can they stand such that no two women stand next to each other?
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  2. #2
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    The men can arrange themselves in 6! ways in a line. Then women can stand in the 5 gaps between the men as well as at the 2 extreme ends of the line, so they can arrange themselves in {\rm^7P_3}=7\times6\times5 ways. Hence the total number of ways of arranging the 9 people is 7\times6\times5\times6!=151\,200.
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  3. #3
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    I was assuming the men were indistinguishable for some reason. Too much Halloween last night
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