Problem

How many different ways can a(n) 12-member jury be selected from 24 possible jury members?

Answer

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Answer

Final Answer: \(\boxed{2704156}\)

Steps

Step 1 :This problem is about selecting a 12-member jury from 24 possible jury members. The order in which we select the jury members does not matter, so this is a combination problem.

Step 2 :In mathematics, a combination is a selection of items without considering the order. 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 select, and '!' denotes factorial, which is the product of all positive integers up to that number.

Step 3 :Here, n = 24 (the total number of possible jury members) and k = 12 (the number of jury members to select).

Step 4 :Substituting these values into the combination formula, we get: \[C(24, 12) = \frac{24!}{12!(24-12)!}\]

Step 5 :Calculating the above expression, we find that there are 2704156 different ways a 12-member jury can be selected from 24 possible jury members.

Step 6 :Final Answer: \(\boxed{2704156}\)

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