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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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35% (01:51) wrong based on 89 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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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.

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

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12 Apr 2017, 20:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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19 May 2017, 10:51

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

This problem can be reworded as "what is the probability that the 2 men are chosen and 2 women are chosen?" So we calculate

4c2 4c2 / 8c4

This format makes it similar to many other problems such as "if there are 8 marbles- 4 red and 4 blue what is the probability of choosing 2 red marbles and 2 blue marbles?"

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