Permutations And Combinations Question 249
Question: The value of $ ^{n}P _{r} $ is equal to [IIT 1971; MP PET 1993]
Options:
A) $ ^{n-1}P _{r}+r{{}^{n-1}}{P _{r-1}} $
B) $ n.{{\ }^{n-1}}P _{r}{{+}^{n-1}}{P _{r-1}} $
C) $ n{{(}^{n-1}}P _{r}{{+}^{n-1}}{P _{r-1}}) $
D) $ ^{n-1}{P _{r-1}}{{+}^{n-1}}P _{r} $
Correct Answer: AShow Answer
Answer:
Solution:
Þ $ \frac{^{n-1}P _{r}}{r!}+\frac{^{n-1}{P _{r-1}}}{(r-1)!}=\frac{^{n}P _{r}}{r!} $
Þ $ ^{n-1}P _{r}+r.{{}^{n-1}}{P _{r-1}}={{}^{n}}P _{r} $ .
BETA
