# Probability that a sample size (of another sample size?) to have certain elements

There are 22 questions from which a teacher can choose for the test. Out of the 22 , the teacher chooses 12 questions for the test of which you answer 10. How many questions do you need to study to ensure that you answer all of them correctly?

I've seen a similar problem on this forum but it was slightly different as the original question count and number of questions studied were given which can be found here.

I feel as if it might be more complex but my thinking process is that because there are 2 questions out of the 12 that can be skipped, the minimum number of questions to require a perfect score would be 20.

• Simply because you study a question does not imply you'll answer it correctly on the test. – StatsStudent May 17 '17 at 5:35
• You're right, Sophie: the other question is slightly different, albeit very closely related. In the present case, it can be helpful to solve a simpler version of the same problem Suppose, for instance, the teacher chooses two questions out of four and you answer one. How many questions would you need to study? Thinking through this version of it might help increase your conviction that this is indeed a simple problem. – whuber May 17 '17 at 13:15