How many solutions are there to the equation: $$x_1 + x_2 + x_3 + x_4 + x_5= 21\;,$$ where $x_i$ is a non-negative integer such that $$0 \le x_1 \le 3;\; 1 \le x_2 < 4;\text{ and }x_3 \ge 15\;?$$
Generalized permutation and combination: number of solutions
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combinatorics