Applications of Polya's theorem to distribution problems and partitions of integers

The number of ways to distribute r identical objects into n identical boxes can usually be obtained by a method of generating function or by a recursive formula. In this paper, for another approach, it is shown that we can obtain this number by using generalization of Polya's theorem. From this, we can also find the number of partitions of integer n as a sum of k positive integers. Computing for the results is discussed.