You want to make five-letter codes that use the letters a, f,e, r, and m without repeating any letter. what is the probability that a randomly chosen code starts with m and ends with e?

The theoretical definition of the probability is

1. The number of all possible outcomes.

You have 5 letters. The first letter of the code can be chosen in 5 ways, the second - in 4 ways, the third - in 3 ways, the fourth letter - in 2 ways and the last one - in 1 way. In total, the number of all possible outcomes is

2. The number of all favorable outcomes.

If the code starts with M and ends with E, then you can change only second, third and fourth letters of the code. The second letter can be chosen in 3 ways (from letters A, F and R), the third letter - in 2 ways and the fourth letter - in 1 way. In total,  the number of all favorable outcomes is

Then the probability is