To evaluate the expression [tex]\(\frac{9!}{3!}\)[/tex], we need to follow these steps:
1. Understand the factorial notation!: The factorial of a number [tex]\( n \)[/tex] (denoted as [tex]\( n! \)[/tex]) is the product of all positive integers from 1 up to [tex]\( n \)[/tex].
- For example, [tex]\( 4! = 4 \times 3 \times 2 \times 1 = 24 \)[/tex].
2. Calculate [tex]\( 9! \)[/tex]:
- [tex]\( 9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \)[/tex].
- When you multiply these numbers together, you get [tex]\( 362,880 \)[/tex].
3. Calculate [tex]\( 3! \)[/tex]:
- [tex]\( 3! = 3 \times 2 \times 1 \)[/tex].
- Multiplying these values gives [tex]\( 6 \)[/tex].
4. Divide [tex]\( 9! \)[/tex] by [tex]\( 3! \)[/tex]:
- So, [tex]\(\frac{9!}{3!} = \frac{362,880}{6} \)[/tex].
5. Perform the division:
- Calculate [tex]\( 362,880 \div 6 \)[/tex] to get [tex]\( 60,480 \)[/tex].
Therefore, the value of the expression [tex]\(\frac{9!}{3!}\)[/tex] is [tex]\( 60,480 \)[/tex].
