Q54 / 160 · AP EAMCET 2023 (18 May Shift 2) · Mathematics

A question paper has two sections A and B in which section-A had 8 questions and section- $B$ has 6 questions. A student has to answer a total of 10 questions, choosing atleast 4 questions from section- $A$ and atleast 3 questions from section-B. Then the number of ways a student can answer that paper is

  • A
    800
  • B
    820
  • C
    840
  • Correct answer
    D
    986

Solution

The student may select: (i) (4 out of 8 from A) and (6 out of 6 from B) (ii) (5 out of 8 from A) and (5 out of 6 from B) (iii) (6 out of 8 from A) and (4 out of 6 from B) (iv) (7 out of 8 from A) and ( 3 out of 6 from B) The no, of ways of these selections are:- (i) ${ }^8 \mathrm{C}_4 \times{ }^6 \mathrm{C}_6=70 \times 1=70$ (ii) ${ }^8 \mathrm{C}_5 \times{ }^6 \mathrm{C}_5=56 \times 6=336$ (iii) ${ }^8 \mathrm{C}_6 \times{ }^6 \mathrm{C}_4=28 \times 15=420$ (iv) ${ }^8 \mathrm{C}_7 \times{ }^6 \mathrm{C}_3=8 \times 20=160$ The required no. of ways $=70+336+420+160=986$.

Hence, the correct answer is option: 'D'.

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