Number of ways of selecting $\mathrm{n}$ tickets from $\mathrm{N}$ tickets numbered from $1$ to $\mathrm{N}$ with replacement $={\mathrm{N}}^{\mathrm{n}}$

Now, the largest number on selected tickets must be $\mathrm{k}$. Hence, favorable cases $={\mathrm{k}}^{\mathrm{n}}-{(\mathrm{k}-1)}^{\mathrm{n}}$

Therefore, required probability $=\frac{{\mathrm{k}}^{\mathrm{n}}-{(\mathrm{k}-1)}^{\mathrm{n}}}{{\mathrm{N}}^{\mathrm{n}}}$