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?

Explanation

(a) 3 questions from part I and 5 questions from part II

(b) 4 questions from part I and 4 questions from part II

(c) 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 ` 5_(C_3) times 7_(C_5)` ways.

4 questions from part I and 4 questions from part II can be selected in ` 5_(C_4) times 7_(C_4)` ways.

5 questions from part I and 3 questions from part II can be selected in ` 5_(C_5) times 7_(C_3)` ways.

Thus, required number of ways of selecting questions


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