A student has to answer 10 out of 13 questions in an examination choosing atleast 5 questions from the first 6 questions. The number of choice available to the student is

Step-by-step solution

There are two cases arise. Case I When 5 questions are selected from first 6 questions and next 5 questions are selected from 7 questions. aligned Number of ways & = ^6 C₅ ^7 C₅ & =6 7 6 2 1 & =126 aligned Case II When 6 questions are selected from first 6 questions and next 4 questions are selected from 7 questions. aligned Number of ways & = ^6 C₆ ^7 C₄ & =1 7 6 5 3 2 =35 aligned Required number of ways =126+35=161