Question

In how many different ways can the first, second and third prize winners be selected from a group of 8 people running a race? [assume that there are no ties].

A. 8! / 5!
B. 8! / (5! × 3!)
C. 8!
D. 38
E. 8! / (5! × 3)

Answer 1

The number of different ways to select the top three prize winners from a group of 8 people, with no ties, is calculated using permutations. For 8 people taken 3 at a time, the permutation formula gives us 8! / 5! different arrangements.

Step-by-step explanation:

When determining the number of different ways to select first, second, and third prize winners from a group of 8 people running a race with no ties, we are dealing with permutations. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement. In this case, we want to find the permutation of 8 items taken 3 at a time, since we are only concerned with the top three positions.

The formula for permutations of n items taken r at a time is nPr = n! / (n - r)!. Applying this to our scenario with 8 items (people) and we want to take 3 (top three winners), the calculation would be 8P3 = 8! / (8 - 3)!, which simplifies to 8! / 5!. Therefore, there are 8! / 5! different ways to select the first, second, and third prize winners from a group of 8 people.