Question

An examination consists of a section A, containing 10 short questions, and a section B, containing 5 long questions. Candidates are required to answer 6 questions from section A and 3 questions from section B.Find the number of different selections of questions that can be made if candidates must answer the first 2 questions in section A and the first question in section B.

Answer 1

You must answer the first 2 of A, that leaves 4 more to choose from the remaining 8 of A ----> C(8,4) = 70
You must answer the first of B, that leaves 2 more to choose from the remaining 4 of B ---> C(4,2) = 6

Number of ways to answer the test = 70*6 = 420
(note, that the order in which you answer the questions does not matter, thus you have a combination)