Mock AIME 5 Pre 2005 Problems/Problem 4

Let the number of balls in the 8 boxes be $a_1,a_2,a_3,...,a_8$ . Thus, we have $a_1+a_2+a_3+...+a_8=16$ , where $a_1,a_2,a_3,...,a_8\geq1$ . By stars and bars, the number of ways this is possible is $\binom{16-1}{8-1}=\binom{15}{7}=6435$ , and since $15+7=22$ , the answer is $6435\mod22=\boxed{11}$ . ~AbbyWong