Problem 1
State the question and data structure, apply counting equally likely outcomes with and without order, check assumptions or design conditions, quantify uncertainty, and interpret the result in context.
Faculty solution guide
Counting, Permutations and Combinations
Accept equivalent statistically correct reasoning. Require context, design, assumptions, uncertainty, and limits.
Problem 2
A common error is to report a calculation without identifying the population, design, assumptions, uncertainty, context, or limits on causal and generalizing claims.
Problem 3
A complete response identifies population, cases, variables, parameter or estimand, study design, and conditions for Counting, Permutations and Combinations.
Problem 4
Repair the earliest invalid assumption, display, calculation, or inference; then rerun the interpretation and state how the correction changes the claim.
Problem 5
A strong application defines context, data source, design, analysis plan, uncertainty, and limits on generalization or causation.
Problem 6
Use at least two of: independent recomputation, alternative graph or model, residual/diagnostic check, resampling, sensitivity analysis, subgroup analysis, simulation, or comparison with a known benchmark.