The number of permutations of n dissimilar things taken not more than ‘r&

Question

The number of permutations of n dissimilar things taken not more than ‘r’ at a time, when each thing may occur any number of times is

Options:

A . n(nr−1)n−1)

B . n(nn−nr)n−1)

C . nP1+nP2+⋯⋯+nPr

D . n(n−1)rn−1

Answer: Option A
:
A

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

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