Question

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

• A. 140
• B. 196
• C. 280
• D. 346

Answer 1

The correct option is B 196

As for the given question, two cases are possible.
(i) Selecting four out of first five questions and six out of remaining eight questions we get ${}^5{C}_4{\times }^8{C}_6=140$ choices.
(ii) Selecting five out of first five questions and five out of remaining eight questions we get ${}^5{C}_5{\times }^8{C}_5=56$ choices.
Hence, the total number of choices is 140 + 56 = 196.