Question

A student prepares for an exam by studying a list of 15 problems. She can solve 7 of them. For the exam, the instructor selects 7 problems at random from the list of 15. What is the probability that the student can solve all 7 problems on the exam? (Round your answer to four decimal places.)

Answer 1

x items can be selected from n items by ⁿC_x ways.

So,

7 problems can be selected from 7 known problems by ⁷C₇ = 7 ways.

Total number of ways to select 7 problems from 15 problems = ¹⁵C₇

¹⁵C₇ = 15! / [ (15-7)! * 7! ] = 6435

P(solve all 7 problems) = ⁷C₇ / ¹⁵C₇

= 1 / 6435

= 0.0002