Total number of things =n Repetition of things is allowed and atmost r can be taken at a time. The number of ways of taking 1 thing at a time =boldsymboln The number of ways of taking 2 things at a time =n2 The number of ways of taking 3 things at a time =n3....... The number of ways of taking r things at a time =n′ Total number of permutations of n different things taken not more than r at a time i.e. number of permutations of taking 1,2,....r at a time. =n+n2+n3+...+nr =