Permutations And Combinations Question 110

Question: If $ ^{n+1}C_3=2{{}^{n}}C_2, $ then n = [MP PET 2000; Pb. CET 2002]

Options:

A) 3

B) 4

C) 5

D) 6

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ ^{n+1}C_3=2.{{}^{n}}C_2 $
    Þ $ \frac{(n+1)!}{3!.(n-2)!}=2.\frac{n!}{2!.(n-2)!} $
    Þ $ \frac{n+1}{3.2!}=\frac{2}{2!} $
    Þ $ n+1=6\Rightarrow n=5 $ .