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Probability question

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erin.m.mcelroy
 Post subject: Probability question
 Post Posted: Sat Apr 02, 2011 12:38 pm 
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Course Students


Posts: 3
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected, what is the probability the team will have exactly 2 women?

I've found 2 ways to solve this and get two different answers. I'm trying to figure out which is correct and why the other is not.

1) P (2 women) = (5/8) * (4/7) * (3/6) * (2/6) = 1/14
This assumes you pick exactly 2 women and two men.

2) Total combinations of teams of 4 = 8!/(4!*4!) = 70 teams
Teams with exactly 2 women and 2 men = [5!/(2!*3!)]* [3!/(2!*1!)] = 30 teams
P (2 women) = 30/70 = 3/7
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jnelson0612
 Post subject: Re: Probability question
 Post Posted: Sat Apr 02, 2011 10:07 pm 
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ManhattanGMAT Staff


Posts: 1857
This one is discussed in the CAT forum: cat-3-t6043.html

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Jamie Nelson
ManhattanGMAT Instructor
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