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

As for given question two cases are possible. (i) Selecting 4 out of first five question and 6 out of remaining 8 question $={ }^5 \mathrm{C}_4 \times{ }^8 \mathrm{C}_6=140$ choices. (ii) Selecting 5 out of first five question and 5 out of remaining 8 questions $={ }^5 \mathrm{C}_5 \times{ }^8 \mathrm{C}_5=56$ choices. Therefore, total number of choices $=140+56=196$.