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

Question

The total number of permutations of n ( &#62; 1 ) different things taken not more than r at a time, when each thing may be repeated any number of times is

Aicharya · Accepted Answer

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} (∵ n > 1)

The total number of permutations of n ( > 1 ) different things taken not more than r at a time, when…

Solution

The total number of permutations of n ( &#62; 1 ) different things taken not more than r at a time, when…

Solution

The total number of permutations of n ( > 1 ) different things taken not more than r at a time, when…