Hello, asugirl87!

An instructor gives his class a set of 11 problems and announces

that the next quiz will consist of a random selection of 5 of them.

If a student has figured out how to answer 6 of the problems correctly,

what is the probability the he or she will answer correctly:

(a) All 5 problems?

There are: possible quizzes.

There are ways that the five questions are among the six the student knows.

Therefore: .

(b) At least 4 problems?

"At least four" means 4or5 right.

There are ways that four questions are among the six the student knows.

There are 6 ways that all five questions are among the six the student knows.

Hence, there are: . ways to get 4 or 5 right.

Therefore: .