In a relay race there are five teams A. B, C. D and E.
(a)  What is the probability that A. B and C finish first, second and third, respectively.
(b)  What is the probability that A. B and C are first three to finish (in any order)      
(Assume that all finishing orders are equally likely).

Explanation

To solve the given problem step by step, we will break it down into two parts as outlined in the question.

### Part (a): Probability that A, B, and C finish first, second, and third respectively.

1. **Identify the total number of teams**: There are 5 teams: A, B, C, D, and E.

2. **Determine the total number of possible finishing orders**: Since we are interested in the first three positions, we can use permutations to find the total number of ways to arrange 5 teams in 3 positions. This is given by the formula for permutations:
\[
...