Permutation, Combination or simply the Counting Principle?

Question

Can you please point me in the right direction?  For each of the following questions, would the correct approach be to calculate the permutation or combination, apply the counting principle, or use more than one approach to find the correct answer?

 

1.  There are 24 contestants in the Hunger Games. Citizens at the Capitol placed bets on who would win. How many orders are possible for the first, second, and third person eliminated? Assume that only 1 person can be eliminated at a time. Show your work.

 

2.  Suppose that each of the 24 contestants at the Hunger Games confronts all the other contestants but none die in the process. How many total confrontations would there be for each contestant to confront all the other contestants exactly one time? Use drawings or lists to help organize your thoughts. Show all work.

Answer 1

To point you in the right direction:

 

1. Order counts so permutations is appropriate (the counting principle might also work)

 

2. Order does not count so combinations is appropriate

 

 

Can you take it from here?