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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. In how many wayscan a student select the questions?

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?

Answers (1)

best_answer

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 ^5C_3.^7C_5 ways.

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

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

Hence, required number of ways of selecting questions :

                                    =^5C_3.^7C_5+^5C_4.^7C_4+^5C_5.^7C_3

                                  =\frac{5!}{2!3!}\times \frac{7}{2!5!}+\frac{5!}{1!4!}\times \frac{7}{4!3!}+\frac{5!}{5!0!}\times \frac{7}{3!4!}

                                 =210+175+35

                                 =420

 

 

 

Posted by

seema garhwal

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