Question

At a gymnastics meet, twenty gymnasts compete for first, second, and third place.

How many ways can first, second, and third place be assigned?


Third place has been announced. In how many ways can the remaining two places be assigned?


Third and second places have been announced. In how many ways can first place be assigned?

Answer 1

- Number of ways to assign 1st, 2nd, 3rd from 20: P(20,3) = 20·19·18 = 6,840.

- If 3rd place is fixed, number of ways to assign 1st and 2nd from the remaining 19: P(19,2) = 19·18 = 342.

- If 2nd and 3rd are fixed, ways to assign 1st from the remaining 18: 18.