Find the number of ordered $8$-tuples of nonnegative integers $x_0 < x_1 < x_2 < \cdots < x_7$ such that $\sum_{i=0}^{7} x_i = 99$
The above question clearly cannot be answered with the classic stars and bars, and the substitution $y_i = x_i – i$ doesn't seem to help either. I cannot see how to progress.
Best Answer
Brain malfunction. You are looking for a partition into different parts with 7 parts of the integer 99