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There are 8 students. 4 of them are men and 4 of them are women. If 4 [#permalink]

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06 Apr 2010, 08:30

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A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

62% (02:24) correct
38% (02:00) wrong based on 55 sessions

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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?

Re: There are 8 students. 4 of them are men and 4 of them are women. If 4 [#permalink]

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06 Apr 2010, 08:43

utin wrote:

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

According to me answer shall be= 4/8 * 3/7 * 4/6 * 3/5

Were I am wrong???Please explain

probability that the number of men is equal to that of women so 2 men and 2 women = (4C2*4C2)/8C4 = 18/35 hence A.

Re: There are 8 students. 4 of them are men and 4 of them are women. If 4 [#permalink]

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06 Apr 2010, 16:22

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This post received KUDOS

utin wrote:

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

According to me answer shall be= 4/8 * 3/7 * 4/6 * 3/5

Were I am wrong???Please explain

You calculated probability of one way in which in which 2 men and 2 women can be selected. But there are 6 different ways in which the selection can happen MMWW, MWMW ,MWWM, WWMM, WMWM,WMMW or 4!/2!2! . So you have to multiply the probability with 6.

Re: There are 8 students. 4 of them are men and 4 of them are women. If 4 [#permalink]

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07 Apr 2010, 09:24

crack700 wrote:

utin wrote:

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

According to me answer shall be= 4/8 * 3/7 * 4/6 * 3/5

Were I am wrong???Please explain

You calculated probability of one way in which in which 2 men and 2 women can be selected. But there are 6 different ways in which the selection can happen MMWW, MWMW ,MWWM, WWMM, WMWM,WMMW or 4!/2!2! . So you have to multiply the probability with 6.

6 *4/8 * 3/7 * 4/6 * 3/5 = 18/35

Thanks for clearing my confusion!!! ...thanks a lot...

Re: There are 8 students. 4 of them are men and 4 of them are women. If 4 [#permalink]

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16 Jun 2015, 18:02

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Re: There are 8 students. 4 of them are men and 4 of them are women. If 4 [#permalink]

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16 Jun 2015, 22:41

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Expert's post

utin wrote:

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 B. 16/35 C. 14/35 D. 13/35 E. 12/35

According to me answer shall be= 4/8 * 3/7 * 4/6 * 3/5

Were I am wrong???Please explain

METHOD-1:

Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36

Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70

METHOD-2: Also see the mistake done by the person who posted this question

Probability of First selected person being Man = 4/8 Probability of Second selected person being Man = 3/7 Probability of First selected person being Woman = 4/6 Probability of Second selected person being Woman = 3/5

i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) * [4!/(2!*2!)] = 18/35

The important part for the readers is to understand the reason of multiplying [4!/(2!*2!)] here

When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well

The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!

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Re: There are 8 students. 4 of them are men and 4 of them are women. If 4 [#permalink]

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13 Feb 2016, 17:45

utin wrote:

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 B. 16/35 C. 14/35 D. 13/35 E. 12/35

8C4 = 70

to select 2 men and 2 women, we can in 4C2*4C2 ways, or 36 ways. the probability will thus be 36/70 or 18/35.

A

gmatclubot

Re: There are 8 students. 4 of them are men and 4 of them are women. If 4
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13 Feb 2016, 17:45

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