Problem

How many 8-person juries can be formed from 24 possible candidates?

Answer

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Answer

So, the number of 8-person juries that can be formed from 24 possible candidates is \(\boxed{735471}\).

Steps

Step 1 :This problem is about forming 8-person juries from 24 possible candidates. It is a combination problem because the order in which we choose the candidates does not matter.

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, which is the product of all positive integers up to that number.

Step 3 :In this case, n = 24 and k = 8.

Step 4 :Substituting these values into the formula, we get \(C(24, 8) = \frac{24!}{8!(24-8)!}\)

Step 5 :Calculating this gives a combination of 735471.

Step 6 :So, the number of 8-person juries that can be formed from 24 possible candidates is \(\boxed{735471}\).

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