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# PS: m 15 #18

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Joined: 05 Jan 2009
Posts: 73

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20 Jun 2009, 13:01
A basket contains 3 blue marbles, 3 red marbles, and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted marbles?

(C) 2008 GMAT Club - m15#18

2/21
3/25
1/6
9/28
11/24
SVP
Joined: 29 Aug 2007
Posts: 2426
Re: PS: m 15 #18 [#permalink]

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21 Jul 2009, 09:30
pmal04 wrote:
A basket contains 3 blue marbles, 3 red marbles, and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted marbles?

(C) 2008 GMAT Club - m15#18

2/21
3/25
1/6
9/28
11/24

Each = 3 marbles
Types/color = 3 different color/types of marbles
Total = 9 marbles.

A blue marble can be selected in 3 ways from 3 blue marbles
A red marble can be selected in 3 ways from 3 red marbles
A yellow marble can be selected in 3 ways from 3 yellow marbles
So 3 marbles of each color can be selected in 3x3x3 = 27 ways
3 marbles of any kind can be selected in 9c3 = 84 ways from 9 marbles.

So the prob = (3x3x3)/9c3 = 27/{9x8x7x6!/(6!3!) = 27/84 = 9/28
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Re: PS: m 15 #18   [#permalink] 21 Jul 2009, 09:30
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# PS: m 15 #18

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