Combinatorics
Count anything without listing everything.
- 1PermutationsreadyHow many ways can you line things up? Fill the slots one at a time and multiply the choices.
0% - 2CombinationsreadyWhen order doesn't matter, count the ordered picks and divide out the repeats: that's choosing.
0% - 3Word RearrangementsreadyShuffle the letters of a word and count the different words you can make, even when letters repeat.
0% - 4ProbabilityreadyHow likely is it? Count the outcomes you want, divide by all the outcomes, and multiply along the branches.
0% - 5CaseworkreadyToo tricky to count in one go? Split it into cases that don't overlap, count each one, and add them up.
0% - 6Complementary CountingreadyWhen "at least one" is hard to count, count the opposite and subtract it from the total.
0% - 7Principle of Inclusion Exclusion (PIE)readyCount everything in two or three overlapping groups: add the groups, subtract the overlaps, add back the middle.
0% - 8Stars and BarsreadyShare identical things among different people by lining them up as stars and dropping in bars.
0% - 9Geometric CountingreadyCount triangles, squares, rectangles and paths on a grid by choosing points, lines and letters instead of drawing every shape.
0% - 10RecursionreadySolve a big counting problem by building it up from small ones: each answer is a sum of earlier answers.
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