Shelves Shelf
18 March 2010
Shelves Shelf
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Arrange 15 distinct books onto bookshelf with 3 shelves.what is the probability that the top shelf has 3 books?
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?
top shelf has exactly 3 books
And top is NOT empty, meaning either middle or bottom is empty
i take it that exactly 3 books from 15 distinct books in the top shelf are implied
firstly, P[top shelf empty] = 1/3,
so the specified event can occur only 2/3 of the time
secondly, if the top shelf isn't empty,
there are 2 ways for 1 shelf to be empty [middle and bottom]
thirdly, if we select books for one of the non-empty shelves,
the books for the other shelf automatically get selected,
and there are 15C3 ways to select 3 books for top shelf
fourthly, total # of ways for a pair of non-empty shelves
= 15C1 + 15C2 + ..15C14 = 2^15 - 2
putting the pieces together,
reqd.probability = [2/3][2*15C3 / (2^15 - 2)]
= 0.0185 or 1.85%
@ ur AD
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i hv taken exactly what you hv said in ur AD
