An instructor gives his class a set of 17 problems with the information that the next quiz will consist of a r?

blank: An instructor gives his class a set of 17 problems with the information that the next quiz will consist of a r?
An instructor gives his class a set of 17 problems with the information that the next quiz will consist of a random selection of 8 of them. If a student has figured out how to do 15 of the problems, what is the probability the he or she will answer correctly
(a) all 8 problems?
(b) at least 7 problems?

Answers and Views:

Answer by shhrewd
Total number of ways the teacher can pick 8 problems from 17 = 17C8 = 17! / 9!8! = 24310 ways
Total number of ways the teacher can pick 8 problems from the 15 the student knows = 15C8 = 15! / 7!8!

Answer to part A = [15! / 7!8!] / [17! / 9!8!] = (15! / 17!) * ( 9! / 7! ) = 9*8 / 16*17 = 9/34

For part B, the only way the student will get less than 7 right will be if the teacher chooses the 2 problems the student doesn’t know how to work.
Ways the teacher can do this = 15C6 (you do 17-2 and 8-2 because you assume the teacher already picked the problems the student will miss)
15! / 9!6! = 5005 ways
24310 ways total – 5005 ways that don’t work = 19305 ways that the student will get at least 7 right.