A certain class of 160 students has 40 honor students and 60 athletes. Eighty students in the class do not participate in sports and are not honor students. If a student is selected at random to represent the class, what is the probability that he is both an honor student and an athlete?

Since we have 80 students in the class do not participate in sports and are not honor student, we have this solution:

160 - 80 = 80 students remaining who are honors and athletes

Since we have 40 honor students and 60 are athletes, we have this solution:

40 + 60 - 80 = 20

The probability is shown below:

20 / 160 = 1 / 8.

The answer is 1/8.