Theorem 4.10: Let s be a multiset with objects of k different types where each has an infinite repetition number. Then the number of r-permutations of s is Proof: In constructing a r-permutation of s, we can choose the first item can be an object of any one of the k types. Similarly the second item to be an object of any one of the k types, and so on Since all repetition numbers of s are infinite the number of different choices for any item is always k and does not depend on the choices of any previous Items By the multiplication principle, the r items can be chose in k ways.▪ Theorem 4.10: Let S be a multiset with objects of k different types where each has an infinite repetition number. Then the number of r-permutations of S is k r . ▪ Proof: In constructing a r-permutation of S, ▪ we can choose the first item can be an object of any one of the k types. ▪ Similarly the second item to be an object of any one of the k types, and so on. ▪ Since all repetition numbers of S are infinite, the number of different choices for any item is always k and does not depend on the choices of any previous items. ▪ By the multiplication principle, the r items can be chose in kr ways