Answer :

Given that a student needs to answer 8 questions out of 12 questions in which 5 from part I and 7 from part II.


It is also told that student needs to answer at least 3 questions from each part.


The possible cases are the following:


i. 3 from part I and 5 from part II


ii. 4 from part I and 4 from part II


iii. 5 from part I and 3 from part II


Let us assume the no. of ways of answering be N.


N = (no. of ways of answering 3 questions from part I and 5 from part II) + (no. of ways of answering 4 questions from part I and 4 from part II) + (no. of ways of answering 5 questions from part I and 3 from part II)


N = ((5C3) × (7C5)) + ((5C4) × (7C4)) + ((5C5) × (7C3))


We know that ,


And also n! = (n)(n – 1)......2.1





N = (10 × 21) + (5 × 35) + (35)


N = 420


The no. of ways of answering the question paper is 420.


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