Question

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?

Answer 1

Yes! The correct answer is option C

Explanation:

C. 0.05

Answer 2

The theoretical definition of the probability is

`Pr=\frac{\text{the number of all favorable outcomes}}{\text{the number of all possible outcomes}}.`

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

`5\cdot 4\cdot 3\cdot 2\cdot 1=120.`

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

`3\cdot 2\cdot 1=6.`

Then the probability is

`Pr=(6)/(120)=(1)/(20)=0.05.`