evaluate the expression.\n$\frac{9!}{3!}$\n3\n6\n60,480\n362,874

Explanation:

Step1: Recall factorial definition

The factorial of a non - negative integer $n$, denoted by $n!$, is the product of all positive integers less than or equal to $n$. So, $n!=n\times(n - 1)\times\cdots\times1$. Then $9! = 9\times8\times7\times6\times5\times4\times3\times2\times1$ and $3! = 3\times2\times1$.

Step2: Simplify the fraction

$\frac{9!}{3!}=\frac{9\times8\times7\times6\times5\times4\times3!}{3!}$. Canceling out the $3!$ terms in the numerator and denominator, we get $9\times8\times7\times6\times5\times4$.

Step3: Calculate the product

$9\times8 = 72$, $72\times7=504$, $504\times6 = 3024$, $3024\times5=15120$, $15120\times4 = 60480$.

Answer:

$60,480$