For "at least one" or "at most" problems, calculate Total - Unwanted. Example: from 6 men and 4 women, form a committee of 5 with at least 1 woman = C(10,5) - C(6,5) = 252 - 6 = 246. This is almost always faster than case-by-case counting. Watch for: "at least 2" means subtract "0 or 1" cases from total.