a) If there are 8 runners in a race, how many different placings are possible for first, second, and third place?

Suppose the top 3 places advance to the next race. How many different groups of 3 (out of 8) are possible?

b) How many different reorderings are possible for the 7 letters in the word 'BARBELL'?

c) Suppose there are 15 candidates to form a jury, of which 9 are men and 6 are women.

How many different juries of 7 members can be formed?

How many different juries made up of 4 men and 3 women are possible?