Problem

How many ways can a committee of 2 be selected from a club with 12 members?
A. 2
B. 33
C. 132
D. 66

Answer

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Answer

Final Answer: \(\boxed{66}\)

Steps

Step 1 :This problem is about selecting a committee of 2 members from a club with 12 members. The order in which we select the members does not matter, so this is a combination problem.

Step 2 :The formula for combinations is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Step 3 :In this case, n=12 and k=2.

Step 4 :Substituting these values into the formula, we get \(C(12, 2) = \frac{12!}{2!(12-2)!} = 66\).

Step 5 :So, there are 66 ways to select a committee of 2 from a club with 12 members.

Step 6 :Final Answer: \(\boxed{66}\)

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