# Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y \leq 7$

Using the addition principle of combinatorics, find the number of non-negative integer solutions to $2x + 3y \leq 7$. This problem is found in the book How to Count by Beeler which contains no solutions, so I have no way of verifying the correct solution.

• show us your try – tortue Aug 22 '18 at 6:32

Hint: Add the number of integer solutions of the equation $2x+3y=n$ for $n=1,2,\ldots,7.$
• We want the number of nonnegative integer solutions, so $n$ can be equal to $0$ as well. – N. F. Taussig Aug 22 '18 at 7:20
• yes, if $0$ is an integer – Leox Aug 22 '18 at 7:25