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  • A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.

State whether the statements in True or False.  A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.

Answers (1)

False. 

A candidate can attempt questions in either of the following ways : 

a.2 from group A and 5 from group B 

b.3 from group A and 4 from group B

c.4 from group A and 3 from group B 

d.5 from group A and 2 from group B  

  Number of ways of attempting 7 questions 

\\=6_{C_{2}} * 6_{C_{5}}+6_{C_{3}} * 6_{C_{4}}+6_{C_{4}} * 6_{C_{3}}+6_{C_{5}} * 6_{C_{2}}\\ =2\left(6 c_{2} * 6 c_{5}+6 c_{3} * 6_{c_{4}}\right)=2(15 * 6+20 * 15)=2(90+300)=2 * 390=780

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infoexpert21

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