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) = [tex] \frac{45!}{(45-3)!} [/tex]
P (45,3) = [tex] \frac{45!}{42!} [/tex]
45! = 42! * 43 * 44 * 45
∴ P (45,3) = [tex] \frac{45!}{42!} [/tex] = [tex] \frac{42! * 43 * 44 * 45}{42!} [/tex]
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.
