Q. A student is to answer 10out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
A) 140
B) 196
C) 280
D) 346
Explanation
(b)
Total number of ways$= {\ ^{5}C}_{4} \times {\ ^{8}C}_{6} \times {\ ^{5}C}_{5} \times {\ ^{8}C}_{5}$
$= \frac{5!}{4! \times 1!} \times \frac{8!}{2! \times 6!} + \frac{8!}{5! \times 3!}$
$= \frac{5 \times 8 \times 7}{2} + \frac{8 \times 7 \times 6}{6}$
$= 140 + 56 = 196$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.