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

When we arrange  one thing at a time, the number of possible permutations is n. When we arrange them twoat a time the number of possible permutations are n x n=n2 and so on. Thus, the total number ofpermutations are  n+n2+…+nr=n(nr−1)n−1 [∵n>1]