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Question: Total number of permutations of 'k' different things, in a row, taken not more than 'r' at a time (e...

Total number of permutations of 'k' different things, in a row, taken not more than 'r' at a time (each thing may be repeated any number of times) is equal to

A

kr –1

B

kr

C

kr−1k−1\frac{k^{r} - 1}{k - 1}

D

k(kr−1)(k−1)\frac{k(k^{r} - 1)}{(k - 1)}

Answer

k(kr−1)(k−1)\frac{k(k^{r} - 1)}{(k - 1)}

Explanation

Solution

Total permutations = 0 + k + k2 + k3 + …..+kr

= k(kr−1)(k−1)\frac{k(k^{r} - 1)}{(k - 1)}