Q.7. In an examination, a question paper consists of 12 questions divided into two
parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student
is required to attempt 8 questions in all, selecting at least 3 from each part. In
how many ways can a student select the questions?
It is given that a question paper consists of 12 questions divided in two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively.
A student is required to attempt 8 questions in all, selecting at least 3 from each part.
This can be done as follows:
(i) 3 questions from part I and 5 questions from part II
(ii) 4 questions from part I and 4 questions from part II
(iii) 5 questions from part I and 3 questions from part II
3 questions from part I and 5 questions from part II can be selected in ways.
4 questions from part I and 4 questions from part II can be selected in ways.
5 questions from part I and 3 questions from part II can be selected in ways.
Hence, required number of ways of selecting questions :