Q. $\ ^{n}P_{r} = 3024$ and $\ ^{n}C_{r} = 126$, then $r$ is
A) 5
B) 4
C) 3
D) 2
Explanation
(b)
Given, $\ ^{n}P_{r} = 3024$
$\Rightarrow \ \ \ \ \frac{n!}{(n - r)!} = 3024$
And $\ ^{n}C_{r} = \frac{n!}{r!(n - r)!}$
$\Rightarrow \ \ \ \ \ \ 126 = \frac{3024}{r!}$
$\Rightarrow \ \ \ \ \ r! = 24 = 4!$
$\Rightarrow \ \ \ \ \ r = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.