First slide

Permutations

Question

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

Easy

A

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

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

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

None of these

Solution

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 $n + n^{2} + \dots + n^{r} = \frac{n (n^{r} - 1)}{n - 1} [∵ n > 1]$

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