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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 - Mathematics

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?

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Solution

It is given that the question paper consists of 12 questions divided into two parts – Part I and Part II, containing 5 and 7 questions, respectively.

A student has to attempt 8 questions, selecting at least 3 from each part.

This can be done as follows.

(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 `""^5C_3 xx ""^7C_5`ways.

4 questions from part I and 4 questions from part II can be selected in `""^5C_4 xx ""^7C_4` ways.

5 questions from part I and 3 questions from part II can be selected in `""^5C_5 xx  ""^7C_3` ways.

Thus, required number of ways of selecting questions

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 7 Permutations and Combinations
Q 7 | Page 157
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