The least value of $n$ for which ${ }^{(n-1)} C_2+{ }^{(n-1)} C_3{ }^n C_2$ is

Question

The least value of $n$ for which ${ }^{(n-1)} C_2+{ }^{(n-1)} C_3>{ }^n C_2$ is

Aicharya · Accepted Answer

${ }^{n-1} C_2+{ }^{n-1} C_3>{ }^n C_2$ ${ }^n C_3>{ }^n C_2 \Rightarrow \frac{n !}{3 !(n-3) !}>\frac{n !}{2 !(n-2) !}$ $\Rightarrow \frac{1}{3} \geq \frac{1}{(n-2)}$ $\begin{aligned} & \Rightarrow \mathrm{n}-2>3 \Rightarrow \mathrm{n}>5 \ & \Rightarrow \mathrm{n}=6\end{aligned}$

The least value of $n$ for which ${ }^{(n-1)} C_2+{ }^{(n-1)} C_3>{ }^n C_2$ is

Solution