Counting Tables – A Grid Method for Counting
A counting table organises two sets of choices into rows and columns, so that every combination appears in exactly one cell of the grid. If one set has m options and the other has n options, the table has m rows and n columns – and since every cell represents one unique combination, the total number of combinations is simply the number of cells: m × n.
Tables are an especially clear tool when there are exactly two choices to combine, since the whole set of possibilities is visible at a glance, laid out as a rectangle.
Using a Counting Table
A table with m rows and n columns has m × n cells, each representing one unique combination of the two sets of choices.
A café offers 3 types of coffee and 4 sizes. Using a table with 3 rows and 4 columns, how many coffee orders are possible?
3 × 4 = 12 possible orders.
Real-Life Application
- Seating charts: a grid of rows and seat numbers counts all possible seat assignments.
- Product variants: a table of colours and sizes counts all product combinations a store must stock.
- Multiplication tables: the times table itself is a counting table for pairs of numbers.
Key Takeaways
- A counting table arranges two sets of choices into rows and columns.
- The total number of combinations equals the number of cells: m × n.
- Tables work best when combining exactly two sets of choices.
Practice: Counting Tables
Counting Tables
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