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# probability that the # of men = # of women ?

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Manager
Joined: 29 Jun 2010
Posts: 249
Schools: LBS, Oxford
Followers: 9

Kudos [?]: 30 [0], given: 12

probability that the # of men = # of women ? [#permalink]  09 Jul 2011, 18:45
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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
SVP
Joined: 16 Nov 2010
Posts: 1680
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 348 [0], given: 36

Re: probability that the # of men = # of women ? [#permalink]  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

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Manager
Joined: 25 May 2011
Posts: 163
Followers: 2

Kudos [?]: 44 [0], given: 71

Re: probability that the # of men = # of women ? [#permalink]  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
Manager
Joined: 26 Apr 2011
Posts: 226
Followers: 0

Kudos [?]: 33 [1] , given: 12

Re: probability that the # of men = # of women ? [#permalink]  26 Dec 2011, 05:01
1
KUDOS
4C2*4C2/8C4 =18/35
Re: probability that the # of men = # of women ?   [#permalink] 26 Dec 2011, 05:01
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# probability that the # of men = # of women ?

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