permutations and combinations

Question

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?

Answer 1

First, you have to identify if the problem is permutation or combination. If the the order matters, it's permutation but if not, it's combination. Here there is first and second place, that means the order matters therefore it is permutation and the formula for permutation is:

nPr = n!/(n-r)!

nPr means the permutation of n taken r at a time.

Since you are taking first and second place therefore:

r=2

and you are getting it from 8 runners, therefore:

n=8

then

8P2 = 8!/(8-2)! = 8!/6! = 8*7 = 56 ways to award medals.