Probability using permutations and combinations

Use permutations and combinations to build compatible favorable and total counts. This precalculus probability quiz covers random committees, ordered rankings, tokens sampled with or without replacement, and complementary counting. Single-select and multiselect questions require you to justify the sample-space model as well as calculate a fraction. Detailed explanations show when order matters, when labels matter, and how a seemingly convenient color-based model can lose equal likelihood. Problems progress from direct subset probabilities to constrained arrangements and checking two equivalent counting methods.