Question

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

Answer 1

The given expression is:

`(5!4!)/(7!2!)`

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

Rewrite 7! as shown:

`(5!4!)/(7!2!)=(5!*4!)/((7*6*5!)*2!)`

Rewrite 4! as shown:

`(5!*4!)/((7*6*5!)*2!)=(5!*(4*3*2!))/((7*6*5!)*2!)`

Cancel out common terms in the numerator and denominator:

`\frac{\cancel{5!}*(4*3*\cancel{2!})}{(7*6*\cancel{5!})*\cancel{2!}}=(4*3)/(7*6)=(12)/(42)=(2)/(7)`The answer is 2/7.