To solve the expression [tex]\(\frac{8! - 6!}{3!}\)[/tex], we can follow these steps:
1. Calculate the factorials:
- [tex]\(8!\)[/tex] (8 factorial) is the product of all positive integers up to 8:
[tex]\[
8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320
\][/tex]
- [tex]\(6!\)[/tex] (6 factorial) is the product of all positive integers up to 6:
[tex]\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720
\][/tex]
- [tex]\(3!\)[/tex] (3 factorial) is the product of all positive integers up to 3:
[tex]\[
3! = 3 \times 2 \times 1 = 6
\][/tex]
2. Subtract the value of [tex]\(6!\)[/tex] from [tex]\(8!\)[/tex]:
[tex]\[
8! - 6! = 40320 - 720 = 39600
\][/tex]
3. Divide the result by [tex]\(3!\)[/tex]:
[tex]\[
\frac{39600}{6} = 6600.0
\][/tex]
Therefore, the final values we obtain are:
1. The numerator [tex]\((8! - 6!)\)[/tex] is [tex]\(39600\)[/tex],
2. The denominator [tex]\((3!)\)[/tex] is [tex]\(6\)[/tex],
3. The final result is [tex]\(\frac{39600}{6} = 6600.0\)[/tex].
So, the calculated result of [tex]\(\frac{8! - 6!}{3!}\)[/tex] is [tex]\(6600.0\)[/tex].
