Problem

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Evaluate.
\[
\frac{18 !}{12 !(18-12) !}
\]

The answer is
(Type an integer of a simplified fraction.)

Answer

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Answer

Final Answer: The answer is \(\boxed{18564}\)

Steps

Step 1 :The given expression is a combination formula, which is used to calculate the number of ways to choose a certain number of items from a larger set, 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 = 18 and k = 12. So, we need to calculate: \[C(18, 12) = \frac{18!}{12!(18-12)!}\]

Step 3 :Substituting the values of n and k into the formula, we get: \[C = 18564.0\]

Step 4 :Final Answer: The answer is \(\boxed{18564}\)

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