Counting PrinciplesWhen to multiply and when to add, and the two questions that decide.MathematicsMultiply for choices made one after another. Add forchoices that are mutually exclusive alternatives.Product: n₁ × n₂ × … × nₖ · Sum: n₁ + n₂3 shirts, 4 ties12 outfitsThe product rule.A 4-digit PIN10⁴ = 10000Repetition allowed.Ordering 5 books5! = 120No repetition.THE COMMON MISTAKEAdding when the choices are made in sequenceMultiplying for choices made in sequenceAdd only when the options are alternatives you choose between. Multiply whenyou make one choice and then a further one.Ask two questions before anything else: does the order matter, and mayitems repeat? Those two answers pick the formula.Counting Principleslearnposters.com
Counting Principles — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Counting Principles poster

The rule, 3 worked examples, and the mistake everyone makes.

Ask two questions before anything else: does the order matter, and may items repeat? Those two answers pick the formula.

Questions about the Counting Principles poster

What’s on the Counting Principles poster?
The rule, 3 worked examples, and the mistake everyone makes. Multiply for choices made one after another. Add for choices that are mutually exclus…; Product: n₁ × n₂ × … × nₖ · Sum: n₁ + n₂; 3 shirts, 4 ties = 12 outfits; A 4-digit PIN = 10⁴ = 10000; Ordering 5 books = 5! = 120; Common mistake: Adding when the choices are made in sequence → Multiplying for choice…. Ask two questions before anything else: does the order matter, and may items repeat? Those two answers pick the formula.
Who is the Counting Principles poster for?
Counting Principles belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning discrete mathematics can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Counting Principles poster?
At the start of any counting problem, before reaching for a formula. A wall chart earns its place by being glanceable from where the work is happening, so Counting Principles belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Counting Principles?
The Binomial Theorem, Euler & Hamiltonian Paths and Graph Vocabulary sit alongside Counting Principles in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Binomial TheoremEuler & Hamiltonian PathsGraph Vocabulary
Is the Counting Principles poster free to download and print?
Yes. Counting Principles downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Counting Principles poster print at?
Counting Principles is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Counting Principles loses nothing.Printing guide

Related posters

Charts that sit alongside Counting Principles on the same wall.

Browse every Mathematics poster, or start from the full catalogue.