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

Total number of questions =13 Now of questions to be selected =10 Restriction - At least 4 from first 5 questions are to be selected. Case I If exactly 4 out of first 5 questions are selected. Number of ways of selecting 4 questions from 5 questions = ^5 C₄=5 Remaining 10-4=6 questions are selected from last 13-5=8 questions in ^8 C₆ ways - Number of ways =5 ^8 C₆=140 Case II If exactly 5 out of first 5 questions are selected. Number of ways of selecting 5 out of 5 questions = ^5 C₅=1 Remaining 10-5=5 questions are