A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

Step-by-step solution

As for given question two cases are possible. (i) Selecting 4 out of first five question and 6 out of remaining 8 question = ^5 C ₄ ^8 C ₆=140 choices. (ii) Selecting 5 out of first five question and 5 out of remaining 8 questions = ^5 C ₅ ^8 C ₅=56 choices. Therefore, total number of choices =140+56=196 .