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# Eight friends (Four Males and Four Females) are lined up in

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Current Student
Joined: 31 Aug 2007
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Eight friends (Four Males and Four Females) are lined up in [#permalink]

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30 Mar 2008, 19:33
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Eight friends (Four Males and Four Females) are lined up in row in a movie. What is the probability that your final arrangement alternates gender all the way down?
Current Student
Joined: 31 Aug 2007
Posts: 369
Followers: 1

Kudos [?]: 99 [0], given: 1

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30 Mar 2008, 19:44
LM wrote:
$$2*(4! * 4!)$$

aren't you forgetting a denominator? Also, explanations, as opposed to simply answers, would be more helpful.
Intern
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30 Mar 2008, 20:13
For the denominator, it's 8! .

Think of the 8 spots on the line. For the first spot, you have from 8 friends to choose from to put there, then 7 , then 6, ...

Similarly for the numerator, alternating the 4 male friends gives 4!, same for the female friends, and it could be Male-Female-Male-.... or Female-Male-Female-...

Hence the 2*.
Manager
Joined: 14 Mar 2008
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31 Mar 2008, 14:54
1/35

probability = 8x4x3x3x2x2x1x1 / 8x7x6x5x4x3x2x1
Re: PS probability   [#permalink] 31 Mar 2008, 14:54
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