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# A committee of three is chosen form a group consisting of 5

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Manager
Joined: 27 Jul 2003
Posts: 124
Location: Singapore
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Kudos [?]: 10 [0], given: 0

A committee of three is chosen form a group consisting of 5 [#permalink]  09 Oct 2003, 20:39
A committee of three is chosen form a group consisting of 5 men and 4 women. If the selection is made at random, find the probability that
a. all 3 are women
b. 2 are men
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 716 [0], given: 781

Re: Probability#13 [#permalink]  09 Oct 2003, 23:44
araspai wrote:
A committee of three is chosen form a group consisting of 5 men and 4 women. If the selection is made at random, find the probability that
a. all 3 are women
b. 2 are men

a. all 3 are women

4C3/ 9C3

b. 2 are men

5C2 * 4C1 / 9C3
SVP
Joined: 03 Feb 2003
Posts: 1607
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Kudos [?]: 81 [0], given: 0

a. agree
b. the stem does not specifically say EXACTLY two men, so I think we have to consider 2 cases: 2 men +1 woman, and 3 men.

P=(5C2*4C1+5C3*4C0)/9C3
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 716 [0], given: 781

stolyar wrote:
a. agree
b. the stem does not specifically say EXACTLY two men, so I think we have to consider 2 cases: 2 men +1 woman, and 3 men.

P=(5C2*4C1+5C3*4C0)/9C3

it doesnt say "atleast"..yours assumption goes a bit too far

thanks
praetorian
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Joined: 03 Feb 2003
Posts: 1607
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Kudos [?]: 81 [0], given: 0

It is you who assumes that the third person is a woman.
Negate the assumption: the third person is a man, the conclusion—there are two men—is not harmed. Therefore, your assertion is not an assumption, and we have to consider two cases.
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