Question

If $C(2n,3):C(n,2)$ $=$ $12:1$, then $n$ $=$

• A. $4$
• B. $5$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

$5$

We have,

$C(2n,3):C(n,2)=12:1$

$\Rightarrow \frac{{}^{2n}{C}_3}{{}^n{C}_2}=\frac{12}{1}$

${\Rightarrow }^{2n}{C}_3=12\cdot {}^n{C}_2$

$\Rightarrow \frac{2n(2n-1)(2n-2)}{3!}=12\cdot \frac{n(n-1)}{2!}$

$\Rightarrow \frac{4(2n-1)}{6}=\frac{12}{2}$

$\Rightarrow 2n-1=9$

$\Rightarrow n=5$