To evaluate the expression [tex]\(\frac{9!}{3!}\)[/tex], we'll break it down step by step.
First, understand what the factorial notation means:
- [tex]\(9!\)[/tex] (read as "9 factorial") is the product of all positive integers from 1 to 9.
- [tex]\(3!\)[/tex] (read as "3 factorial") is the product of all positive integers from 1 to 3.
Let's calculate each of these factorials individually:
1. Calculate [tex]\(9!\)[/tex]:
[tex]\[
9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 362880
\][/tex]
2. Calculate [tex]\(3!\)[/tex]:
[tex]\[
3! = 3 \times 2 \times 1 = 6
\][/tex]
Next, we need to divide the result of [tex]\(9!\)[/tex] by the result of [tex]\(3!\)[/tex]:
[tex]\[
\frac{9!}{3!} = \frac{362880}{6} = 60480
\][/tex]
Therefore, the value of the expression [tex]\(\frac{9!}{3!}\)[/tex] is [tex]\(\boxed{60480}\)[/tex].
