You learned the two fundamental counting rules:
Sum rule: Add when choices are mutually exclusive (OR)
Product rule: Multiply when choices are independent (AND)
You handled restrictions with complementary counting (total minus invalid). You used the pigeonhole principle to prove existence. You corrected overlaps with inclusion-exclusion.
You counted passwords, paths on grids, and letter combinations. These principles are the foundation for all combinatorics. Next: permutations and combinations.