Question

question 10 of 10 at a competition with 8 runners, 2 medals are awarded for first and second place. each medal is different. how many ways are there to award the medals? a. 64 b. 40,320 c. 28 d. 56

Explanation:

Answer:

D. 56

To determine the number of ways to award 2 different medals (first and second place) to 8 runners, we use permutations (since the order matters: first place is different from second place). The formula for permutations of \( n \) items taken \( k \) at a time is \( P(n, k) = \frac{n!}{(n - k)!} \).

Here, \( n = 8 \) (runners) and \( k = 2 \) (medals). Plugging in the values:
\( P(8, 2) = \frac{8!}{(8 - 2)!} = \frac{8!}{6!} = \frac{8 \times 7 \times 6!}{6!} = 8 \times 7 = 56 \).

Thus, the number of ways to award the medals is 56, corresponding to option D.