probability question

Question

Aidan needs to clean his room, and is arranging the following school books on his bedroom shelf : Math, Science, English, French, and History. If he randomly stands the five books next to each other on the shelf, what is the probability that the History and Science books will be on the two ends

Answer 1

There are 5! = 120 permutations

 

 For History first and Science last, there are 3! ways to arrange the books

 LIkewise for Science first and History last, there are 3! ways to arrange the books.

 

2 x 3! = 12

 

So 12 of the 120 possible permutations results in a probability of

 

12/120 = 1/10 = 0.1 = 10%