Q. $\ ^{47}C_{4} + \sum_{r = 1}^{5}{\ \ }\ ^{52 - r}C_{3}$ is equal to
A) $\ ^{45}C_{6}$
B) $\ ^{52}C_{5}$
C) $\ ^{52}C_{4}$
D) None of these
Explanation
(c)
$\ ^{47}C_{4}\sum_{r = 1}^{5}{\ \ }\ ^{52 - r}C_{3}$
$= \ ^{51}C_{3} + \ ^{50}C_{3} + \ ^{49}C_{3} + \ ^{48}C_{3} + \ ^{47}C_{3} + \ ^{47}C_{4}$
$= \ ^{51}C_{3} + \ ^{50}C_{3} + \ ^{49}C_{3} + \ ^{48}C_{3} + \ ^{48}C_{4}$
$= \ ^{51}C_{3} + \ ^{50}C_{3} + \ ^{49}C_{3} + \ ^{49}C_{4}$
$= \ ^{51}C_{3} + \ ^{50}C_{3} + \ ^{50}C_{4}$
$= \ ^{51}C_{3} + \ ^{51}C_{4} + \ ^{52}C_{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.