Systematic counting

Recognise the model, justify the rule and solve independently.

Decide whether order matters and whether repetition is allowed before you start counting.

Split a count into cases that do not overlap and together cover every possibility, then add the counts.

Count the complement by subtracting the unwanted outcomes from the total, using the same kind of outcome in both counts.

Find the largest selection that still fails, and explain why one more object guarantees the required result.