Chapter 8, Problem 9CR

To determine

To find: The simplified value of the given factorial expression.

Answer to Problem 9CR

The value of the given factorial expression is $\frac{1}{132}$ .

Explanation of Solution

Given: The given factorial expression is $\frac{10!}{12!}$ .

Concept Used: The factorial of a number is defined as a product of all the natural numbers starting from the given number till 1. Hence mathematically, the factorial of n is defined as-

  $n!=n\times (n-1)\times (n-2)\times \mathrm{....}\times 3\times 2\times 1$

Also, the factorial of a number can expressed as the factorial of another number lesser than the given number in the following way-

  $n!=n\times (n-1)!$

  $=n\times (n-1)\times (n-2)!$

  $=n\times (n-1)\times (n-2)\times (n-3)!$ and so on.

Calculations: The given factorial expression can be simplified as-

  $\frac{10!}{12!}$

  $=\frac{10!}{12\times 11\times 10!}$

  $=\frac{1}{12\times 11}$

  $=\frac{1}{132}$

Hence, the simplified value is $\frac{1}{132}$ .