Printable worksheets

Six free worksheets for classrooms and self-study, each with a free answer key. Open one, press Print, and hand it out. They build from counting to simulation.

Worksheet 1 · Ages 12+ · 20 min
Counting arrangements (permutations)
Seven questions on factorials and ordered selections from a deck.
Open and print Answer key
Worksheet 2 · Ages 13+ · 25 min
Choosing cards (combinations)
Eight questions that build up to the 2,598,960 five-card hands.
Open and print Answer key
Worksheet 3 · Ages 12+ · 20 min
Probability of a single draw
Eight questions on events, 'or', 'not' and drawing twice without replacement.
Open and print Answer key
Worksheet 4 · Ages 14+ · 25 min
The 'at least one' trick
Six questions using the complement to avoid long case-by-case counting.
Open and print Answer key
Worksheet 5 · Ages 14+ · 25 min
Averages and expected value
Seven questions on long-run averages with abstract 'points' and simple counts.
Open and print Answer key
Worksheet 6 · Ages 14+ · 35 min
Simulation lab: experiment vs theory
A hands-on lab: run the hand simulator at four sample sizes and compare with the exact answer.
Open and print Answer key

How to use these worksheets

Work through them in order: counting, choosing, probability, “at least one”, expected value, then the simulation lab.
Pair each worksheet with the matching lesson. The calculator lets students check their arithmetic.
The hand rankings chart works as a classroom poster for the counting examples.
The simulation lab uses a fixed seed so every student gets identical results, which makes marking easy.

Cards are used only as a counting model: nothing is staked or won in any activity.

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