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An examination paper consists of 12 questions divided into two parts A and B.
Part A contains 7 questions and Part B contains the remaining questions. A candidate required to attempt 8 questions selecting at least 3 from each part. In how many ways can the candidate select the question​

Respuesta :

mhanifa

Answer:

  • 420 ways

Step-by-step explanation:

There are 3 possible scenarios

1) 5 questions from A and 3 questions from B:

  • [tex]_7C_5*_5C_3=7!/5!2!*5!/3!2! = (6*7)/2*(4*5)/2=210[/tex]

2) 4 questions from each part:

  • [tex]_7C_4*_5C_4=7!/4!3!*5!/4!1! = (5*6*7)/(2*3)*5=175[/tex]

3) 3 questions from A and 5 questions from B:

  • [tex]_7C_3*_5C_5=7!/4!3!*1 = (5*6*7)/(2*3)=35[/tex]

Total number of ways:

  • 210 + 175 + 35 = 420

Answer:

Student has to do 8 questions such that he does at least 3 questions from both the sets

How can he go about (Set I, Set II)  =(3,5) or (4,4) or (5,3)

So, total number of ways of doing this is given by 

[tex]5c_{3} \times 7c_{5} + 5c_{4} \times 7c _{4} + 5c_{5} \times 7c _{3}[/tex]

[tex] = (10)(21) + (5)(35) + (1)(35) = 210 + 210 = 420[/tex]

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