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The total number of permutations of n different things taken not more than r at a time when each thing may be repeated any number of times is

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$\frac{n (n^{r + 1} - 1)}{n - 1}$

$\frac{n^{r + 1} - 1}{n - 1}$

$\frac{n (n^{r} - 1)}{n - 1}$

$\frac{n^{r} - 1}{n - 1}$

answer is C.

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Detailed Solution

$n + n^{2} + n^{3} + - - - + n^{r} = n \frac{(n^{r} - 1)}{n - 1}$

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