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 permutation or a combination, and then find the number of ways to award the medals

permutation; 720 ~apex

There are 720 ways to award the medals

Step-by-step explanation:

* Lets explain the difference between permutations and combinations

- Both permutations and combinations are collections of objects

- Permutations are for lists (order matters)

- Combinations are for groups (order doesn't matter)

- A permutation is an ordered combination.

- Permutation is nPr, where n is the total number and r is the number

of choices

# Example: chose the first three students from the group of 10

students, n = 10 and r = 3, then 10P3 is 720

- Combinations is nCr, where n is the total number and r is the number

of the choices

# Example: chose a group of three students from the group of 10

students n = 10 and r = 3, then 10C3 is 120

* Lets solve the problem

- There are six runner

- There are 6 medals awarded for first place through sixth place

- Each medal is different

- The order is important because they arranged from 1st position to

the 6th position

∴ We will use the permutation

∵ There are 6 medals for 6 runners

∵ 6P6 = 6 * 5 * 4 * 3 * 2 * 1 = 720

∴ There are 720 ways to award the medals