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Difficult Math Question #41 - Probability

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800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Question #41 - Probability

Post Mon Oct 30, 2006 11:36 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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    ajith Legendary Member
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    Post Mon Oct 30, 2006 10:06 pm
    4 people can be selected from 8 in 8c4 ways = 70
    now for no: of men and women to be equal, the no: should be 2.
    we can select 2 women from 4 in = 4c2 =6 ways
    2 men from 4 can also be selected in 6 ways
    so the total no: of ways=6*6=36

    req probability= 36/70 =18/35

    A it is! Smile

    rajs.kumar Senior | Next Rank: 100 Posts Default Avatar
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    Post Tue Oct 31, 2006 2:10 am
    2 men and 2 women can be selected from 4 men and 4 women in 4c2 x 4c2 ways = 36

    Total number of ways in which 4 people can be chosen from 8 is 8c4.

    Probability = 36/70

    Answer is A

    800guy Master | Next Rank: 500 Posts Default Avatar
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    Post Wed Nov 01, 2006 10:58 am
    OA:

    there has to be equal no of men & women so out of 4 people selected there has to be 2M & 2W.
    Total ways of selecting 4 out of 8 is 8C4
    total ways of selecting 2 men out of 4 is 4C2
    total ways of selecting 2 women out of 4 is 4C2

    so probability is (4C2*4C2)/ 8C2 = 18/35

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