Chapter 8, Problem 4CT

To determine

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

Answer to Problem 4CT

The value of the given factorial expression is 7920.

Explanation of Solution

Given: The given factorial expression is $\frac{11!\times 4!}{4!\times 7!}$ .

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-

  $\frac{11!\times 4!}{4!\times 7!}$

  $=\frac{11!}{7!}$

  $=\frac{11\times 10\times 9\times 8\times 7!}{7!}$

  $=11\times 10\times 9\times 8$

  $=7920$

Hence, the simplified value is 7920.