The total number of permutations of n (>1) different things taken not more that r at a time, whena thing may be repeated any number of times, is

When k(1≤k≤r) things are arranged, the number of possible arrangements, when repetition is allowed is n×n×……×n⏟k times =nkThus, the total possible arrangements isn+n2+n3+…+nr=nnr−1n−1