SOLUTION: A box contains 12 red marbles, 7 green marbles, and 9 black marbles. A sample of 9 marbles is to be picked from the box. (a) How many samples contain at least 1 red marble? (b)

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Question 1023986: A box contains 12 red marbles, 7 green marbles, and 9 black marbles. A sample of 9 marbles is to be picked from the box.
(a) How many samples contain at least 1 red marble?
(b) How many samples contain exactly 4 red marbles and exactly 3 black marbles?
(c) How many samples contain exactly 7 red marbles or exactly 6 green marbles?
(d) How many samples contain exactly 5 green marbles or exactly 3 black marbles?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A box contains 12 red marbles, 7 green marbles, and 9 black marbles. A sample of 9 marbles is to be picked from the box.
(a) How many samples contain at least 1 red marble?
Total # of 9 marble samples:: 28C9
Total # of 9 marble samples with no red:: 16C9
Ans: # of 9 marble samples with at least one red:: 28C9-16C9
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(b) How many samples contain exactly 4 red marbles and exactly 3 black marbles?
Ans: 12C4*9C3*7C2
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(c) How many samples contain exactly 7 red marbles or exactly 6 green marbles?
Ans: 12C7*16C2 + 7C6*21C3
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(d) How many samples contain exactly 5 green marbles or exactly 3 black marbles?
Ans: 7C5*21C4 + 9C3*19C6
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Cheers,
Stan H.
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