The total number of permutations of n (> 1) Different things taken not more than r at a time, when each thing may be repeated any number of times is

When we arrange  one thing at a time, the number of possible permutations is n. When we arrange them two
at a time the number of possible permutations are n x n=n² and so on. Thus, the total number of
permutations are  $\mathrm{n}+{\mathrm{n}}^2+\dots +{\mathrm{n}}^{\mathrm{r}}=\frac{\mathrm{n}({\mathrm{n}}^{\mathrm{r}}-1)}{\mathrm{n}-1}[\because \mathrm{n}>1]$