A student prepares for an exam by studying a list of 10 prob

A student prepares for an exam by studying a list of 10 problems. She can Solve 8 of them. For the exam, the instructor selects 7 questions at random from the list of 10. What is the probability that the student can Solve all 7 problems on the exam? (Enter an exact number as an integer, fraction, or decimal.)

Solution

probality = (8 known, get 7) / (10 total, get 7) = ⁸C₇ /¹⁰C₇

= [8!/7!]/[10!/(7!3!]

= [8!]*6/[10*9*8!]

= 6/90

= 2/30 = 1/15