Question

Evaluate.

9!/7!

A.) 63
B.) 72
C.) 81

Answer 1

B.) 72

Step-by-step explanation

Recall the expansion for the factorial notation:

`n! = n * (n - 1) * (n - 2) * ...3 * 2 * 1`

We want to simplify

`(9!)/(7!)`

Let us expand the numerator up to 7! while maintaining the denominator.

`\implies \: (9 * 8 * 7!)/(7!)`

When we cancel out the common factors,we obtain:

`\implies \: (9 * 8 * 1)/(1)`

This simplifies to

`\implies \: (72)/(1) = 72`

The correct answer is B.