A question paper has two sections A and B in which section-A had 8 questions and section- $B$ has 6…
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
800
820
840
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 $=70+336+420+160=986$.