Question 581549: A box contains 11 red balls, 9 green balls, and 9 black balls. A sample of 9 is to be picked from the box.
(a) How many samples contain at least 1 red ball?
9966385 samples
(b) How many samples contain exactly 4 red balls and exactly 3 black balls?
997920 samples
(c) How many samples contain exactly 5 green balls or exactly 3 black balls?
I need to figure this last part of the problem out and I know that (C(9,5)*C(20,4))+(C(9,3)*C(20,6))-(C(9,5)*C(9,3)) is the format I need but I can't seem to get the correct answer out of it.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A box contains 11 red balls, 9 green balls, and 9 black balls. A sample of 9 is to be picked from the box.
(a) How many samples contain at least 1 red ball?
Total number of samples: 29C9
Total number with no red: 18C9
Number with at least 1 red: 29C9-18C9 = 9966385 samples
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(b) How many samples contain exactly 4 red balls and exactly 3 black balls?
11C4 * 9C3 * 9C2 = 997920 samples
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(c) How many samples contain exactly 5 green balls or exactly 3 black balls?
9C5 * 9C3 * 11C1 = 116424
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Cheers,
Stan H.
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