Question

There are 5 swimmers in a race. There will be a first-place and a second-place prize awarded. In how many different ways can the 2 prizes be awarded?

Answer 1

It would be 20, because;
1 - 2 / 3 / 4 / 5
2 - 1 / 3 / 4 / 5
3 - 1 / 2 / 4 / 5
4 - 1 / 2 / 3 /5
5 - 1 / 2 / 3 / 4

= 4x5 = 20

Answer 2

Answer: so we have 5 positions, but we only care for the first two.

So, in the first position there are 5 options (because there are 5 swimmers).

In the second position whe will have 4 options (because there are already one swimmer in the first position).

So you have 5*4 = 20 ways for the prizes to be awarded.