যদি ${ }^{n} P_{r}=336$ এবং ${ }^{n} C_{r}=56$ হয়, তবে n = ?

$\frac{{ }^{n} P_{r}}{{ }^{n} C_{r}}=\frac{336}{56}$ $\begin{array}{l}\Rightarrow \frac{\mathrm{r}^{\mathrm{n}} \cdot \mathrm{C}_{\mathrm{r}}}{{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{T}}}=6 \\\Rightarrow\lfloor\mathrm{r}=\lfloor 3 \therefore \mathrm{r}=3 \\\therefore{ }^{\mathrm{n}} \mathrm{P}_{3}=\mathrm{n}(\mathrm{n}-1)(\mathrm{n}-2)=336=8.7 .6={ }^{8} \mathrm{P}_{3} \\\therefore \mathrm{n}=8\end{array}$