Question

A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals. How many ways can 3 runners earn gold, silver and bronze medals?

Answer 1

This is a Permutation question solved by P (n,r).

n (Number of objects) = 45
r (Number of samples) = 3

P (n,r) = P (45,3)


P (45,3) = $\frac{45!}{(45-3)!}$

P (45,3) = $\frac{45!}{42!}$

45! = 42! * 43 * 44 * 45

∴ P (45,3) = $\frac{45!}{42!}$ = $\frac{42! * 43 * 44 * 45}{42!}$

P (45,3) = 43 * 44 * 45

= 85,140

Therefore, in a group of 45 runners, 3 people can earn gold, silver and bronze medals in 85,140 ways.


p.s - This question should be under Mathematics, not Geography.