In how many ways can 3 prefects be chosen out of 8 prefects?

There are different ways to approach this problem, but one common method is to use the formula for combinations. In general, the number of ways to choose k items out of n distinct items (without repetition and without order) is given by the formula: \(\binom{n}{k} = \frac{n!}{k!(n-k)!}\) where n! (read as "n factorial") means the product of all positive integers up to n, and 0! is defined as 1. In this specific problem, we want to choose 3 prefects out of 8, so we have: \(\binom{8}{3} = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56\) Therefore, there are 56 ways to choose 3 prefects out of 8 prefects. So the answer is: 56.