Ace the Academic Team Math Challenge 2025 – Power Up Your Problem-Solving Skills!

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How many ways can four people be selected at random from a committee of twenty people?

2,000

4,845

To determine how many ways four people can be selected from a committee of twenty, we use the concept of combinations, as the order in which the individuals are selected does not matter. The formula for combinations is given by:

\[ C(n, r) = \frac{n!}{r!(n - r)!} \]

where \( n \) is the total number of items to choose from, \( r \) is the number of items to choose, and "!" denotes factorial, which is the product of all positive integers up to that number.

In this case, we are selecting 4 people from a total of 20. Thus, we set \( n = 20 \) and \( r = 4 \). Now, substituting these values into the combinations formula gives:

\[ C(20, 4) = \frac{20!}{4!(20 - 4)!} = \frac{20!}{4! \cdot 16!} \]

This simplifies to:

\[ C(20, 4) = \frac{20 \times 19 \times 18 \times 17}{4 \times 3 \times 2 \times 1} \]

Calculating the

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10,240

15,060

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