Q. $\ ^{n - 2}C_{r}{+ 2}^{n - 2}C_{r - 1} +^{n - 2}C_{r - 2}$equals
A) $\ ^{n + 1}C_{r}$
B) $\ ^{n}C_{r}$
C) ${\ \ }^{n}C_{r + 1}$
D) $\ ^{n - 1}C_{r}$
Explanation
(b)
$\ ^{n - 2}C_{r} + 2 \bullet \ ^{n - 2}C_{r - 1} + \ ^{n - 2}C_{r - 2}$
$= \left( \ ^{n - 2}C_{r} + \ ^{n - 2}C_{r - 1} \right) + \left( \ ^{n - 2}C_{r - 1} + \ ^{n - 2}C_{r - 2} \right)$
$= \ ^{n - 1}C_{r} + \ ^{n - 1}C_{r - 1}$ $\left( \therefore\ ^{n}C_{r - 1} + \ ^{n}C_{r} = \ ^{n + 1}C_{r} \right)$
$= \ ^{n}C_{r}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.