Question

How many ways can 2 Geometry books, 8 Algebra books and 2 Pre-Calculus books be arranged on a shelf if all the books of each respective subject are identical?

Answer 1

Answer: 2,970

Step-by-step explanation:

The number of ways to arrange n things such that a things are identical , b things are identical , and so on is  $\dfrac{n!}{a!\cdot b!\cdot ....}$ .

As per given , we have

Number of Geometry books = 2

Number of Algebra books = 8

Number of Pre-Calculus books =2

Total books = 2+8+2=12

Then, the number of ways to arrange them : $\dfrac{12!}{2!\cdot 8!\cdot 2!}$

$=\dfrac{12\times11\times10\times9\times8!}{2\times8!\times2}=2970$

Hence, the total number of ways to arrange 2 Geometry books, 8 Algebra books and 2 Pre-Calculus books is 2,970.