SMO Open · 11. Counting and probability
Count with the right model: multiply, choose, shift, group by residues, exclude overlaps, recurse, then turn counts into probabilities.
Choose between ordered and unordered counting and divide by symmetries correctly.
Use combinations, stars and bars and shifts (bijections) to count solutions and subsets.
Count with residue classes and inclusion–exclusion.
Set up recurrences by the last step and compute probabilities through complements.