Question

MEDALLLLL!!!
1There are 100 runners entered in a marathon. How many different groups of three runners can finish in first, second, and third?

Does this problem involve permutations or combinations?

2There are 100 runners entered in a marathon. Trophies are awarded for first place, second place, and third place. In how many different ways could the runners receive trophies?

Does this problem involve permutations or combinations?

Answer 1

The question states "groups of 3". In other words A first, B second and C third is exactly the same group of three as B first C second and A third. Where order of selection doesn't matter you use combinations. Where order of selection does matter you use permutations.

Therefore the answer = 100C3 or choose any three from 100
= 100! / (3!97!)
= (100 * 99 * 98 * 97!) / (3 *2 * 1 *97!)
= 100* 99 * 98 /6
= 161700

Answer 2

You would do the second part the same way

Answer 3

yes?

Answer 4

you would do it the same way

Answer 5

Thanks

Answer 6

:)