Question

In an examination, a question paper consists of 12 questions divided into two parts, 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?

Answer 1

We have, 

Number of questions in the question paper = 12 

Number of questions in part 1 = 5 

Number of question in part II = 7 

Number of questions to attempt = 8 

Condition: Selecting at least 3 from each part

Part I(out of 5)	Part I(out of 7)	Number of ways
3	5	5C3 x 7C5
4	4	5C4 x 7C4
5	3	5C5 x 7C3

∴ Required number of ways of selecting questions