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# A small company employs 3 men and 5 women. If a team of 4

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Joined: 29 Jun 2008
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A small company employs 3 men and 5 women. If a team of 4 [#permalink]  15 Jul 2008, 09:08
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

a. 1/14
b. 1/7
c. 2/7
d. 3/7
e. 1/2

---- My (wrong) solution follows: ---

The probability to choose 1 woman out of the group: 5/(3+5) = 5/8
Then, the probability to choose another woman after the first one was chosen: 4/(3+4) = 4/7
Then, the probability to choose one man after two woman were chose: 3/(3+3) = 3/6
Then, the probability to choose another man is: 2/(2+3) = 2/5
Multiplies those probabilites gives (5/8)*(4/7)*(3/6)*(2/5) = 1/14

I was pleased to see it was one of the options and not so pleased to see it is wrong. I will appreciate an explanation as to what is wrong with my solution.
Current Student
Joined: 28 Dec 2004
Posts: 3387
Location: New York City
Schools: Wharton'11 HBS'12
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Re: Men and Women [#permalink]  15 Jul 2008, 09:58
nirimblf wrote:
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

a. 1/14
b. 1/7
c. 2/7
d. 3/7
e. 1/2
?:

total possible ways of picking 4 people..8C4

now how many ways to choose men..3C2 and same for women 4C2

3c2*4c2/8c4 =3/7
Senior Manager
Joined: 07 Jan 2008
Posts: 298
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Re: Men and Women [#permalink]  15 Jul 2008, 10:08
we need 2 women and 2 men, a total of 4 people:
5c2*3C2/8C4 = 10*3/70 = 3/7 (D) [2 women out of 5; 2 men out 4; 4 people out of 8]
Re: Men and Women   [#permalink] 15 Jul 2008, 10:08
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# A small company employs 3 men and 5 women. If a team of 4

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