Question

evaluate the expression.$\frac{9!}{3!}$○ 3○ 6○ 60,480○ 362,874

Explanation:

Step1: Define factorial rule

Recall that $n! = n\times(n-1)\times\cdots\times1$. So we can expand the numerator:
$9! = 9\times8\times7\times6\times5\times4\times3!$

Step2: Simplify the fraction

Substitute the expanded form into the expression to cancel $3!$:
$\frac{9!}{3!} = \frac{9\times8\times7\times6\times5\times4\times3!}{3!} = 9\times8\times7\times6\times5\times4$

Step3: Calculate the product

Compute step-by-step:
$9\times8=72$; $72\times7=504$; $504\times6=3024$; $3024\times5=15120$; $15120\times4=60480$

Answer:

60,480