How many officers can be selected?

Question

A dance team has three officers- colonel, lieutenant and captain. How many groups of officers can be selected from the 20 members

Answer 1

This deals with permutations, since each officer position is unique.

So, for the first position, you'd have 20 members to choose from. Assuming a member can't hold more than one officer position, we know that the second position would only have 19 members to choose from and the third would have 18 members.

Using this logic, the total amount of arrangements for these officer positions is:

20*19*18 = 6840

Answer 2

This problem is a p(20 select 3) = 20!/(20-3)! = 20*19*18 = 6840