Find the number of solutions of the equation $x_1+x_2+x_3+x_4=9$ (or 18)!

Question

how many solutions $(x_1,x_2,x_3,x_4)$ are there to the equation $x_1+x_2+x_3+x_4=18$, $1\leq x_1<x_2<x_3<x_4\leq 9$, $x_1,x_2,x_3,x_3\in\mathbb{N}$. Thanks so much!

Answer 1

Here are all solutions: $$(\text{x1}=1\land \text{x2}=2\land \text{x3}=6\land \text{x4}=9)\lor (\text{x1}=1\land \text{x2}=2\land \text{x3}=7\land \text{x4}=8)\lor (\text{x1}=1\land \text{x2}=3\land \text{x3}=5\land \text{x4}=9)\lor (\text{x1}=1\land \text{x2}=3\land \text{x3}=6\land \text{x4}=8)\lor (\text{x1}=1\land \text{x2}=4\land \text{x3}=5\land \text{x4}=8)\lor (\text{x1}=1\land \text{x2}=4\land \text{x3}=6\land \text{x4}=7)\lor (\text{x1}=2\land \text{x2}=3\land \text{x3}=4\land \text{x4}=9)\lor (\text{x1}=2\land \text{x2}=3\land \text{x3}=5\land \text{x4}=8)\lor (\text{x1}=2\land \text{x2}=3\land \text{x3}=6\land \text{x4}=7)\lor (\text{x1}=2\land \text{x2}=4\land \text{x3}=5\land \text{x4}=7)\lor (\text{x1}=3\land \text{x2}=4\land \text{x3}=5\land \text{x4}=6)$$