Q. If $\ ^{n - 1}C_{3} + \ \ ^{n - 1}C_{4} > \ ^{n}C_{3}$, then $n$ is just greater than integer
A) 5
B) 6
C) 4
D) 7
Explanation
(d)
$\ ^{n - 1}C_{3} + \ ^{n - 1}C_{4} > \ ^{n}C_{3}$
$\Rightarrow \ \ \ \ \ \ ^{n}C_{4} > \ ^{n}C_{3}$
$\Rightarrow \ \ \ \ \frac{n!}{(n - 4)!4!} > \frac{n!}{(n - 3)!3!}$
$\Rightarrow \ \ \ (n - 3)(n - 4)! > (n - 4)!4$
$\Rightarrow \ \ \ n > 7$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.