k এর কোন মানের জন্য ${ }^{n} P_{r}=k\left({ }^{n+1} C_{r}-{ }^{n} C_{r-1}\right)$ হবে?

${ }^{n} P_{r}=k\left({ }^{n+1} C_{r}-{ }^{n} C_{r-1}\right)$ $\begin{array}{l}\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{T}} \times \mathrm{r} !=\mathrm{k}\left({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{T}}+{ }^{\mathrm{n}}\mathrm{C}_{\mathrm{r}-1}-{ }^{\mathrm{n}}\mathrm{C}_{\mathrm{T}-1}\right) \\\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \times \mathrm{r} !=\mathrm{k} \times{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \therefore \mathrm{k}=\mathrm{r} !\end{array}$