Why don't you show your attempt and answers to the first problem?

Suppose the set of all questions and the subset of five exam questions are fixed. The sample space consists of subsets with 6 questions that the student knows. Obviously, there are such subsets.

In how many ways can we select 6 questions out of 8 so that all five exam questions are there? We have to select the 5 exam questions (only one option), and the remaining 6th question can be any of the 3 non-exam questions.

In how many ways can we select 6 questions out of 8 so that exactly 4 exam questions are there? We need to select 4 questions out of the 5 exam questions, and select the remaining 2 out of 3 non-exam questions.