Question

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

Explanation:

Step1: Recall the formula for factorial

The factorial of a non - negative integer \(n\), denoted as \(n!\), is defined as \(n!=n\times(n - 1)\times(n - 2)\times\cdots\times1\) for \(n\geq1\) and \(0!=1\).

We need to evaluate \(\frac{9!}{3!}\). First, expand \(9!\) and \(3!\) using the factorial formula.

\(9!=9\times8\times7\times6\times5\times4\times3!\) (because \(9! = 9\times8\times7\times6\times5\times4\times3\times2\times1\) and \(3! = 3\times2\times1\), so we can write \(9!\) as \(9\times8\times7\times6\times5\times4\times3!\))

Step2: Simplify the fraction

\(\frac{9!}{3!}=\frac{9\times8\times7\times6\times5\times4\times3!}{3!}\)

The \(3!\) terms in the numerator and the denominator cancel out.

Now, calculate \(9\times8\times7\times6\times5\times4\):

\(9\times8 = 72\)

\(72\times7=504\)

\(504\times6 = 3024\)

\(3024\times5=15120\)

\(15120\times4 = 60480\)

Answer:

\(60480\) (which corresponds to the first option "60,480")