Question

If ${}^{n-1}{C}_3+{}^{n-1}{C}_4>{}^n{C}_3$, then the least value of $n$ is

• A. 7
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is B 8

Using ${}^n{C}_r{+}^n{C}_{r-1}{=}^{n+1}{C}_r$
${}^{n-1}{C}_3{+}^{n-1}{C}_4{=}^n{C}_4{>}^n{C}_3$

$\Rightarrow n>4+3=7$, where $n$ is a natural number
Hence, least possible value of $n$ is $8$.