# Calculating probability from a given situation using combinations.

A class is given a list of 20 study problems from which 10 will be part of an upcoming exam. If a given student knows how to solve 15 of the problems, find the probability that the student will be able to answer,

a. All 10 questions on the exam

b. Exactly 8 questions on the exam

c. At least 9 questions on the exam

#### Solution Preview

...s the probability is

(15!/(10!5!))/(20!/(10!10!))=(10*9*8*7*6)/(20*19*18*17*16)

=21/(4*19*17)=1.63%

b. The student can answer exactly 8 questions. So 8 questions are chosen from 15 problems and 2 questions are chosen from 5 ...