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