Theorem 4.12: Lets=looa1oo'a2,., oo ak. Then the number of r-combinations of s equals c(ktr-lg r) Proof. ( lThe number of r-combinations of s equals the number of solutions of the equation Ex,=r where x1,x2,., Xk are non-negative integers (2)We show that the number of these solutions equals the number of permutations of the multiset={(k-1)·0,r·1}▪ Theorem 4.12: Let S ={·a1 ,·a2 ,…, ·ak }. Then the number of r-combinations of S equals C(k+r-1,r)。 ▪ Proof. (1)The number of r-combinations of S equals the number of solutions of the equation ▪ where x1 ,x2 ,…,xk are non-negative integers x r k i  i = =1 (2)We show that the number of these solutions equals the number of permutations of the multiset T={(k-1)·0,r·1}