Permutations And Combinations Question 109

Question: Value of r for which $ ^{15}{C _{r+3}}={{}^{15}}{C _{2r-6}} $ is [Pb. CET 1999]

Options:

A) 2

B) 4

C) 6

D) - 9

Show Answer

Answer:

Correct Answer: C

Solution:

  • Either $ r+3=2r-6 $ or $ r+3+2r-6=15,(\because {{}^{n}}C _{r}={{}^{n}}{C _{n-r}}) $
    Þ $ r=9 $ or $ r=6 $ .

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