An urn contains seven red balls, seven white balls, and seven blue balls, and sample of five balls is drawn at random without replacement. Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)

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An urn contains seven red balls, seven white balls, and seven blue balls, and sample of five balls is drawn at random without replacement. Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)

Mathematics
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I have half of the answer. C (21,5) = 20,349 do I multiply by 3? i also need to use C (7,5) = 21 I thought the answer was \[\frac{ 5 \times 21 }{20,349}\approx0.0051\] But it is wrong
all of the same color means "all red OR all white OR all blue"
so \[3\times \frac{\binom{7}{5}}{\binom{21}{5}}\]

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oh yeah sorry i didn't read carefully YES multiply by 3
permutation problem rather than a combination problem since the balls aren't replaced
?
you get the same answer no matter which way you go it
\[\frac{7\times 6\times 5\times 4\times 3}{21\times 20\times 19\times 18\times 16}\]same as \[\frac{\binom{7}{5}}{\binom{21}{2}}\]
thank you I will calculate right now
you can just multiply your answer above by 3
I got 0.3999 and it was wrong. :_(
I got it!!! =0.0031
thank you for all your help Satellite73

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