Question

At a competition with 6 runners, 6 medals are awarded for first place through

sixth place. Each medal is different. How many ways are there to award the

medals?

Decide if the situation involves a permutation or a combination, and then find

the number of ways to award the medals.

O

A. Permutation; number of ways = 720

O

B. Combination; number of ways = 720

O

c. Combination; number of ways = 1

O

D. Permutation; number of ways = 1

Answer 1

Answer:

A. Permutation; number of ways = 720

Step-by-step explanation:

For the first medal, we have 6 runners that can earn it.  

For the second medal, we have 5 runners because there's one who won the first one.

For the third, we have 4 runners.

And so on up to the 6th medal where we have just one runner left.

As this happens all at the same time, we have to multiply them.

Ways to award the medals = 6*5*4*3*2*1 = 6! = 720

Remember that a permutation is a combination where the order matters. So, in this case, is a permutation because each medal is different.