SOLUTION: Arrange 15 different books onto bookshelf with 3 shelves. what is the probability that the top shelf has three books under the condition that exactly one shelf is empty? I'm don

Question 246505: Arrange 15 different books onto bookshelf with 3 shelves. what is the probability that the top shelf has three books under the condition that exactly one shelf is empty?
I'm don't know how to use the condition. Any help?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Arrange 15 different books onto bookshelf with 3 shelves. what is the probability that the top shelf has three books under the condition that exactly one shelf is empty?
I don't know how to use the condition. Any help?
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P(A | B) = P(A and B)/P(B)
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P(3 on top | 1 empty) = P(3 on top AND one empty)/P(1 empty)
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# of ways to get 3 on top: 15C3
# of ways to pick one empty: 2
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# of ways to pick 3 on top AND one empty = 2*15C3
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# of ways to Place 3 without restriction: 15!
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P(1 empty) = 2/3
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P(3 on top | 1 empty) = (2*15C3/15!)/(2/3) = 4.639x10^-10
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Check this out carefully. I am not fully satisfied with it.
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Cheers,
Stan H.
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