Question

Evaluate5! 4!____7! 2!Simplify as much as possible

Answer 1

The given expression is:

$\frac{5!4!}{7!2!}$

It is required to simplify the expression as much as possible.

Rewrite 7! as shown:

$\frac{5!4!}{7!2!}=\frac{5!\times4!}{(7\times6\times5!)\times2!}$

Rewrite 4! as shown:

$\frac{5!\times4!}{(7\times6\times5!)\times2!}=\frac{5!\times(4\times3\times2!)}{(7\times6\times5!)\times2!}$

Cancel out common terms in the numerator and denominator:

$\frac{\cancel{5!}\times(4\times3\times\cancel{2!})}{(7\times6\times\cancel{5!})\times\cancel{2!}}=\frac{4\times3}{7\times6}=\frac{12}{42}=\frac{2}{7}$The answer is 2/7.