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?
The student can choose 3 questions from part I and 5 from part II
Or
4 questions from part I and 4 from part II
5 questions from part 1 and 3 from part II
3 questions from part I and 5 from part II can be chosen in
= 5C3 × 7C5
4 questions from part I and 4 from part II can be chosen in
= 5C4 × 7C4
5 questions from part 1 and 3 from part II can be chosen in
= 5C5 × 7C3
Now the total number of ways in which a student can choose the questions are = 210 + 175 + 35 = 420