Combinations with ripetition

Hi,everyone .Let a no-empty set ,suppose is finite and let ,natural , its cardinality ,let a natural number : we say every ordinate -upla is a disposition with repetition of class k of where .To define a combination with repetition of class of i gave the following deinition: let , two dispositions with repetition of class of .We say and are "of the same type" if , and ,set ,where r is the cardinality of , we have . So we can consider the following set every disposition with repetion of class k of and are "of the same type" and observe R is an equivalence relation on every disposition with repetiton of class k of } ,so we can say disposition with repetition of class k of } , , the equivalence class of on every disposition with repetition of class k of } modulo is a combination with repetition of class k of .Is this definition already used ?