To find the value of the expression [tex]\(\frac{8! - 6!}{3!}\)[/tex], let's go through the steps in detail:
1. Calculate [tex]\(8!\)[/tex]:
[tex]\(8!\)[/tex] which is pronounced as "8 factorial," is the product of all positive integers from 1 to 8:
[tex]\[
8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320
\][/tex]
2. Calculate [tex]\(6!\)[/tex]:
Similarly, [tex]\(6!\)[/tex] is calculated as:
[tex]\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720
\][/tex]
3. Calculate [tex]\(3!\)[/tex]:
And [tex]\(3!\)[/tex] is:
[tex]\[
3! = 3 \times 2 \times 1 = 6
\][/tex]
4. Compute the numerator [tex]\(8! - 6!\)[/tex]:
We subtract [tex]\(6!\)[/tex] from [tex]\(8!\)[/tex]:
[tex]\[
8! - 6! = 40320 - 720 = 39600
\][/tex]
5. Divide the result by [tex]\(3!\)[/tex]:
Now, we divide the result from step 4 by [tex]\(3!\)[/tex]:
[tex]\[
\frac{8! - 6!}{3!} = \frac{39600}{6} = 6600
\][/tex]
Thus, the value of the expression [tex]\(\frac{8!-6!}{3!}\)[/tex] is:
[tex]\[
\boxed{6600}
\][/tex]
