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# A black sack contains three green balls, five yellow balls,

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A black sack contains three green balls, five yellow balls, [#permalink]

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03 Jul 2003, 13:30
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A black sack contains three green balls, five yellow balls, and four white ones. Three balls are taken at random without repetition. What is the probability of having all the the three balls of different colors?

An easy stuff for night rumination...
Intern
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03 Jul 2003, 20:55
Here's what I got:
3/12 * 5/11 * 4/10 = 1/22

stolyar wrote:
A black sack contains three green balls, five yellow balls, and four white ones. Three balls are taken at random without repetition. What is the probability of having all the the three balls of different colors?

An easy stuff for night rumination...
SVP
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Posts: 1603
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Kudos [?]: 229 [0], given: 0

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03 Jul 2003, 22:58
This is an example of so-called classical hypergeometrical distribution:

3C1*5C1*4C1/12C3 = 3/11
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05 Jul 2003, 11:29
Stolyar, is this approach fair?:

3 G, 5Y, 4W

P(green) = 3/12
and
p(yellow) = 5/11
and
p(white) = 4/10

(3/12)x(5/11)x(4/10) = 1/22

Then because the 3 colors could be drawn out 3! ways:

3! x (1/22) = 6/22 = 3/11
SVP
Joined: 03 Feb 2003
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06 Jul 2003, 12:38
JP wrote:
Stolyar, is this approach fair?:

3 G, 5Y, 4W

P(green) = 3/12
and
p(yellow) = 5/11
and
p(white) = 4/10

(3/12)x(5/11)x(4/10) = 1/22

Then because the 3 colors could be drawn out 3! ways:

3! x (1/22) = 6/22 = 3/11

your approach is legal, but mine is quicker (I think so)
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