To evaluate the expression [tex]\(\frac{9!}{3!}\)[/tex], follow these steps:
1. Understanding Factorials:
- [tex]\(9!\)[/tex] (read as "9 factorial") means multiplying all positive integers up to 9. Therefore, [tex]\(9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)[/tex].
- Similarly, [tex]\(3!\)[/tex] (read as "3 factorial") means multiplying all positive integers up to 3. Therefore, [tex]\(3! = 3 \times 2 \times 1\)[/tex].
2. Calculate the Factorials:
- [tex]\(9! = 362,880\)[/tex]
- [tex]\(3! = 6\)[/tex]
3. Substitute the Factorials into the Expression:
- [tex]\(\frac{9!}{3!} = \frac{362,880}{6}\)[/tex]
4. Perform the Division:
- When you divide 362,880 by 6, you get 60,480.
So, the value of the expression [tex]\(\frac{9!}{3!}\)[/tex] is [tex]\(60,480\)[/tex].
