Permutation and Combination

Question

The debate club has 12 members. All the members' names go in the hat for selection of captain and captain's assistant. In how many ways can the two positions be filled?

Answer 1

There are 12 possibilities for the captain, which removes one person and leaves 11 possibilities for captain's assistant.

 

So we have 12 * 11 = 132 possibilities.

 

This is a permutation without repetition problem.

The formula here is n! / (n - k)!

Where n = 12 and k = 2.