- Break into chunks and then add back together.
- Break into tasks and then multiply together.
- Do via the back door – find exactly when you don’t want and what’s left over is what you do want. Combining this with DeMorgan’s Laws can be powerful.
- Counting: find the total number of ways to accomplish a task and subtract the number of ways that don’t meet your criteria.
- Probability: take 1 and subtract the probability of what you want not happening.
- Restrict your viewpoint: if you have 5 pencils in 750 million writing utensils, and you want to know how many ways there are to choose a sample of 3 of the 5 pencils, ignore the rest of the 750 million and compute 5 choose 3.
- Get rid of overlap: the inclusion-exclusion principle shows up in many different guises.