Q. 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
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
Explanation
(c)
When we arrange one things at a time, the number of possible permutations is $n.$ When we arrange them two at a time the number of possible permutations are $n \times n = n^{2}$
and so on. Thus, the total number of permutations are
$n + n^{2} + .... + n^{r} = \frac{n(n^{r} - 1)}{n - 1}\ \ \ (\because n > 1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.