Use counting rules to determine the probability.
-Dave puts a collection of 15 books on a bookshelf in a random order. Among the books are 2 fiction and 13 nonfiction books. What is the probability that the 2 fiction books will be all together on the Left side of the shelf and the 13 nonfiction all together on the right side of the shelf?
A)0.00952
B)0.01809
C)0.01333
D)0.01619

Question

Use counting rules to determine the probability.
-Dave puts a collection of 15 books on a bookshelf in a random order. Among the books are 2 fiction and 13 nonfiction books. What is the probability that the 2 fiction books will be all together on the Left side of the shelf and the 13 nonfiction all together on the right side of the shelf? 
A)0.00952
B)0.01809
C)0.01333
D)0.01619

Quizplus · Accepted Answer

The probability is calculated by considering the arrangement where the 2 fiction books are together on the left and the 13 nonfiction books are on the right. There are 2! ways to arrange the fiction books among themselves and 13! ways to arrange the nonfiction books. Since there are 15! total ways to arrange all books without any restrictions, the probability is (2! * 13!) / 15!, which simplifies to 1/105 or approximately 0.00952.

Use Counting Rules to Determine the Probability