Permutations And Combinations Question 115

Question: If $ ^{43}{C _{r-6}}={{}^{43}}{C _{3r+1}}, $ then the value of r is [Kerala (Engg.) 2002]

Options:

A) 12

B) 8

C) 6

D) 10

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given, $ ^{43}{C _{r-6}}={{}^{43}}{C _{3r+1}} $
    Þ $ r-6=3r+1 $ or $ r-6+3r+1=43 $
    Þ $ r=-\frac{7}{2} $ (impossible) or $ r=12 $ .