Question 847454: if eight different books are arranged at random in a shelf, what is the probability that a certain pair of books
(a) will be beside each other? (b) will not be together?
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! a) For this, let's take the long approach.
There are 8! different ways to arrange all the books. Let's say we are looking at books 1,2,3,4,5,6,7,8 and we want to know the probability that 3 and 7 [there is no significance to those numbers] are next to each other.
Let's look at all the templates. 37###### 73###### #37##### #73##### ##37#### ##73#### ###37### ###73### ####37## ####73## #####37# #####73# ######37 ######73
14 different templates.
So we have 14/8! = .000034
b) We are just talking about the complement, so take 1-.0003 and get .9997.
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