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# Combinations and permutations question watch

1. heres the question:

Three married couples, Mr & Mrs Lee, Mr & Mrs Martin, and Mr & Mrs Shah, stand in a line for a photograph to be taken. Find the number of different ways in which these six people can be arranged if no man stands next to another man.

Whenever I try this question I get 72 (3! x 3! x 2!) as the answer but apparantly the answer should be 144. Can anyone tell me where I'm going wrong?

Thanks.
2. the possibliities are
M W M W M W = 3! * 3!
W M W M W M = 3! * 3!
M W W M W M = 3! * 3!
M W M W W M = 3! * 3!
total = 144
3. (Original post by Retropmot)
no
the possibliities are
M W M W M W = 3! * 3!
W M W M W M = 3! * 3!
M W W M W M = 3! * 3!
M W M W W M = 3! * 3!
total = 144
Oh yes - thanks I forgot about the second two possibilities!

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Updated: April 10, 2006
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