The problem can be solved using the concept of permutations.

In this case, we have 7 runners and we want to know in how many ways we can award 2 different medals (for first and second place).

This is a permutation problem because the order in which the medals are awarded matters (a first place is not the same as a second place).

The formula for permutations is:

P(n, r) = n! / (n-r)!

where:
- n is the total number of items,
- r is the number of items to choose,
- "!" denotes factorial, which is the product of all positive integers up to that number.

So, in this case, we have:

P(7, 2) = 7! / (7-2)!

Calculating the factorials:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
5! = 5 * 4 * 3 * 2 * 1 = 120

So,

P(7, 2) = 5040 / 120 = 42

Therefore, there are 42 ways to award the medals. So, the answer is D.42.

Question

The problem can be solved using the concept of permutations.

In this case, we have 7 runners and we want to know in how many ways we can award 2 different medals (for first and second place).

This is a permutation problem because the order in which the medals are awarded matters (a first place is not the same as a second place).

The formula for permutations is:

P(n, r) = n! / (n-r)!

where:
- n is the total number of items,
- r is the number of items to choose,
- "!" denotes factorial, which is the product of all positive integers up to that number.

So, in this case, we have:

P(7, 2) = 7! / (7-2)!

Calculating the factorials:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
5! = 5 * 4 * 3 * 2 * 1 = 120

So,

P(7, 2) = 5040 / 120 = 42

Therefore, there are 42 ways to award the medals. So, the answer is D.42.

Knowee AI · Accepted Answer