For what of n is n+1C3 = 4(nC3)?

For what of n is ⁿ⁺¹C₃ = 4(ⁿC₃)?

Correct Answer: Option D

Explanation

(^{n+1}C_3 = 4(^nC_3)\frac{(n+1)!}{(n+1-3)!3!} = 4left(frac{n!}{(n-3)!3!}right)\frac{(n+1)n!}{(n-2)(n-3)!}=4left(frac{n!}{n-3!}right)\=frac{n+1}{n-2}=frac{4}{1}\n+1 = 4(n-2)\n+1 = 4n-8\-3n = -9\frac{-9}{-3}\n=3)