生成函數的問題

1.Determine the number of positive integer solutions of x1 + x2 + x3 + x4 + x5 = 45 where xi must be exactly divided by 3 for i = 1,2,3,4,5

Ans : A(x) = (x^3 + x^6 + x^9 + ..... ) ^ 5，為何不是 (1 + x^3 + x^6 + x^9 + ..... ) ^ 5，0不是被所有數整除嗎？

2.Suppose we need to count the strings of length 7 over the alphabet A = {c,d,e,n,q,s,u} that ends with either s or c and contains both q and u in sequence. Please count the total number of strings

這題是P4-41範例1用指數生成函數解，A(x) = (e^x - 1)^2 (e^x)^5，這樣的解法有辦法確定s或c在字尾嗎？

3.Find the number of n-digit words generated from the alphabet {0,1,2,3,4} in each of which the total number of 0's and 1's is even

這題解答是寫說0和1的總和為偶數，可是英文題意看起來好像是0為偶數個且1為偶數個的狀況，是我英文有問題嗎？若題目改成是0或1為偶數的話，英文會是怎麼寫呢？