Combinatorics and Graph Theory · Problem 2.1.1

Inclusion-Exclusion — David Guichard

Mathematics — Combinatorics · inclusion-exclusion-submultisets

Problem

List all 6 solutions to the restricted equation in example 2.1.1 (i.e.,

x_1 + x_2 + x_3 = 7

with

0 \leq x_1 \leq 2

0 \leq x_2 \leq 4

0 \leq x_3 \leq 3

), and list the corresponding 6 submultisets.