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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: 122
Location: Singapore
A committee of three is chosen form a group consisting of 5 [#permalink]

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09 Oct 2003, 21:39
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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: 3454

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10 Oct 2003, 00:44
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: 1604

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13 Oct 2003, 23:43
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: 3454

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14 Oct 2003, 00:19
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
SVP
Joined: 03 Feb 2003
Posts: 1604

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14 Oct 2003, 00:35
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.
14 Oct 2003, 00:35
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