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 don't know how to use the condition. Any help?
-----------------------
P(A | B) = P(A and B)/P(B)
-----------------------------
P(3 on top | 1 empty) = P(3 on top AND one empty)/P(1 empty)
---
# of ways to get 3 on top: 15C3
# of ways to pick one empty: 2
---
# of ways to pick 3 on top AND one empty = 2*15C3
---
# of ways to Place 3 without restriction: 15!
---
P(1 empty) = 2/3
-------------------------
P(3 on top | 1 empty) = (2*15C3/15!)/(2/3) = 4.639x10^-10
==========================================================
Check this out carefully.  I am not fully satisfied with it.
==========================================================
Cheers,
Stan H.