Question

If ${}^{n-1}{C}_3{+}^{n-1}{C}_4{>}^n{C}_3$ , then $n$ is just greater than integer

• A. 5
• B. 6
• C. 4
• D. 7

Answer 1

Answer: (D)

${}^{n-1}{C}_3+{}^{n-1}{C}_4>{}^n{C}_3$
$\Rightarrow {}^n{C}_4>{}^n{C}_3$
$\left[\because {}^n{C}_r+{}^n{C}_{r+1}={}^{n+1}{C}_{r+1}\right]$
$\Rightarrow \frac{n!}{4!(n-4)!}>\frac{n!}{3!(n-3)!}$
$\Rightarrow \frac{1}{4}>\frac{1}{(n-3)}$
$\Rightarrow n-3>4$
$\Rightarrow n>7$