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probability that the # of men = # of women ?

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Senior Manager
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Joined: 29 Jun 2010
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probability that the # of men = # of women ? [#permalink] New post 09 Jul 2011, 18:45
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 3 sessions
There are 8 students. 4 of them are men and 4 of them are women. If 4 students
are selected from the 8 students. What is the probability that the number of men is
equal to that of women?


A.18/35
B16/35
C.14/35
D.13/35
E.12/35
[Reveal] Spoiler: OA
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Re: probability that the # of men = # of women ? [#permalink] New post 09 Jul 2011, 20:23
Probability that the number of men is
equal to that of women = 2 men and 2 women are selected

= 4C2 * 4C2/8C4

= 4!/(2!2!) * 4!/(2!2!)/8!/(4!4!)

= (4*3*2!/(2!2!))^2/(8*7*6 *5*4!/4!/4!)


= 36/(2*35)

= 18/35

Answer - A
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Re: probability that the # of men = # of women ? [#permalink] New post 23 Dec 2011, 11:52
The only possibility is that 2 men and 2 women make the group.

P=\frac{C^4_2*C^4_2}{C^8_4}=\frac{18}{35}


A
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Re: probability that the # of men = # of women ? [#permalink] New post 26 Dec 2011, 05:01
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4C2*4C2/8C4 =18/35
Re: probability that the # of men = # of women ?   [#permalink] 26 Dec 2011, 05:01
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