Question 2 of 17, Step 1 of 1
Correct
Evaluate the following expression.
\[
\frac{10 !}{8 !(10-8) !}
\]
Answer
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Step 1 ：The given expression is a combination formula, which is used to calculate the number of ways to choose a smaller group from a larger group without regard to the order of selection. The formula is given by: \[C(n, k) = \frac{n!}{k!(n-k)!}\] where: n is the total number of items, k is the number of items to choose, n! is the factorial of n, k! is the factorial of k, and (n-k)! is the factorial of (n-k).

Step 2 ：In this case, n = 10 and k = 8. So we need to calculate: \[C(10, 8) = \frac{10!}{8!(10-8)!}\]

Step 3 ：By substituting the values of n and k into the formula, we get: \[C = 45.0\]

Step 4 ：Final Answer: The value of the given expression is \(\boxed{45}\)