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A container holds 6 marbles that are red, 5 that are blue, and 4 that are white. If 4 marbles are drawn at random without replacement, what is the probability that the selection includes at least one marble of each colour?
- 48/91
- 44/91
- 88/91
- 24/91
Correct answer: 48/91
Solution
With 4 marbles drawn from 6+5+4=15, the favourable colour counts are the (2,1,1) splits. Summing C(6,r)C(5,b)C(4,w) over all such splits gives 720 favourable out of C(15,4)=1365, i.e. 720/1365 = 48/91.
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