Agroup 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?

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) = 

P (45,3) = 

45! = 42! * 43 * 44 * 45

∴ P (45,3) =  = 

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.