The theoretical definition of the probability is
[tex]Pr=\dfrac{\text{the number of all favorable outcomes}}{\text{the number of all possible outcomes}}.[/tex]
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
[tex]5\cdot 4\cdot 3\cdot 2\cdot 1=120.[/tex]
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
[tex]3\cdot 2\cdot 1=6.[/tex]
Then the probability is
[tex]Pr=\dfrac{6}{120}=\dfrac{1}{20}=0.05.[/tex]
