A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 question is

Step-by-step solution

The total number of questions is 12, divided into two groups of 6 questions each. Let the groups be A and B, each containing 6 questions. The candidate needs to select 7 questions in total, with the constraint that no more than 5 questions can be selected from either group. Let x be the number of questions selected from group A and y be the number of questions selected from group B. We have x + y = 7 and the constraints x 5 and y 5 . Possible pairs (x, y) satisfying these conditions are: 1. x = 2, y = 5 : The numbe