Q. A question paper is divided into two parts $A$ and $B$ and each part contain 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part is
A) 80
B) 100
C) 200
D) None of these
Explanation
(c)
The number of ways that the candidate may select
(i) if 2 questions from $A$ and 4 question from $B$
$= \ ^{5}C_{2} \times \ ^{5}C_{4} = 50$
(ii) 3 question from $A$ and 3 questions from $B$
$= \ ^{5}C_{3} \times \ ^{5}C_{3} = 100$
and (iii) 4 questions from $A$ and 2 questions from $B$
$= \ ^{5}C_{4} \times \ ^{5}C_{2} = 50$
Hence, total number of ways $= 50 + 100 + 50 = 200$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.