To solve the problem [tex]\(\frac{10!}{(10-3)!}\)[/tex], let's break it down step-by-step:
1. First, we need to understand the notation:
- [tex]\(10!\)[/tex] (read as "10 factorial") means the product of all positive integers up to 10. Mathematically, this is [tex]\(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)[/tex].
- [tex]\((10-3)!\)[/tex] or [tex]\(7!\)[/tex] (read as "7 factorial") means the product of all positive integers up to 7. Mathematically, this is [tex]\(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\)[/tex].
2. Now let's determine the values of these factorials:
- [tex]\(10! = 3,628,800\)[/tex]
- [tex]\(7! = 5,040\)[/tex]
3. Next, we substitute these values back into the given expression:
[tex]\[
\frac{10!}{(10-3)!} = \frac{10!}{7!}
\][/tex]
4. Substituting the calculated values:
[tex]\[
\frac{3,628,800}{5,040}
\][/tex]
5. Finally, we perform the division to find the result:
[tex]\[
\frac{3,628,800}{5,040} = 720
\][/tex]
Hence, the value of [tex]\(\frac{10!}{(10-3)!}\)[/tex] is 720.
Therefore, the correct answer is:
A. 720
