Example: What is the number of integeal solutions of the equation 1+x2+x3=5 which satisfy0≤x1s2,0≤x2S2,l≤x3≤5? Solution: We introduce new variables X=X-1 3 and our equation becomes X+x2+x3=4 The inequalities on the xi and x3 are satisfied if and only if 0≤x1≤2,0≤x2≤2,0≤x3≤4. 4- combinations of multiset{2·a,2b,4·e}▪ Example: What is the number of integeal solutions of the equation ▪ x1+x2+x3=5 ▪ which satisfy 0x12,0x22,1x35? ▪ Solution: We introduce new variables, ▪ x3 '=x3 -1 ▪ and our equation becomes x1+x2+x3 '=4. ▪ The inequalities on the xi and x3' are satisfied if and only if ▪ 0x12,0x22, 0x3 '4. ▪ 4-combinations of multiset {2·a,2·b,4·c}