Question

1. if a race has 10 competitors and you want to know the number of ways to arrange the top 3 finishers, what should you calculate?

the number of permutations of 10 taken 3 at a time.
the number of combinations of 10 taken 3 at a time.
the total number of competitors.
the average position of finishers.
clear all

Explanation:

To determine the number of ways to arrange the top 3 finishers out of 10 competitors, we need to consider the order of the finishers (since first, second, and third places are distinct). Permutations are used when the order of selection matters, while combinations are used when order does not matter. Here, the order of the top 3 finishers is important (e.g., first place is different from second place). So we need to calculate the number of permutations of 10 taken 3 at a time. The other options are incorrect: combinations don't consider order, the total number of competitors is just 10 (not related to arranging top 3), and the average position is not relevant to counting arrangements.

Answer:

A. The number of permutations of 10 taken 3 at a time.