Question

If ${}^{(n-1)}{C}_3{+}^{(n-1)}{C}_4{>}^n{C}_3$, then the minimum value of $n$ is:

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (D)

8

${}^{(n-1)}{C}_3{+}^{(n-1)}{C}_4{>}^n{C}_3$,

Use ${}^n{C}_{r-1}{+}^n{C}_r{=}^{n+1}{C}_r$

$\Rightarrow \frac{n!}{(n-4)!4!}>\frac{n!}{(n-3)!3!}$

$\Rightarrow \frac{1}{4}>\frac{1}{n-3}$

$\Rightarrow n-3>4\Rightarrow n>7$

Smallest value of $n=8$