Worksheets · Geometry

Geometry counting principle worksheet

If one thing can happen in m ways and the next in n ways, together they happen in m times n ways. That one sentence is the whole topic, and it is what permutations and combinations are built on.

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Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Counting Principle

Date Period

Answer each question.

  1. How many outcomes are there from a spinner with 5 equal parts, then a card drawn from 52, then a ten-sided die?
  2. How many outcomes are there from a ten-sided die, then a four-sided die?
  3. How many outcomes are there from a spinner with 5 equal parts, then a coin, then a spinner with 8 equal parts?
  4. How many outcomes are there from a spinner with 5 equal parts, then a coin?
  5. How many outcomes are there from a four-sided die, then a six-sided die?
  6. How many outcomes are there from a spinner with 8 equal parts, then a ten-sided die?
  7. How many outcomes are there from a spinner with 8 equal parts, then a spinner with 5 equal parts?
  8. How many outcomes are there from a ten-sided die, then a four-sided die, then a spinner with 8 equal parts?
  9. How many outcomes are there from a ten-sided die, then a coin, then a four-sided die?
  10. How many outcomes are there from a six-sided die, then a ten-sided die?
  11. How many outcomes are there from a six-sided die, then a coin, then a ten-sided die?
  12. How many outcomes are there from a card drawn from 52, then a spinner with 8 equal parts, then a four-sided die?
  13. How many outcomes are there from a card drawn from 52, then a ten-sided die?
  14. How many outcomes are there from a ten-sided die, then a card drawn from 52, then a coin?
  15. How many outcomes are there from a four-sided die, then a card drawn from 52?
  16. How many outcomes are there from a spinner with 8 equal parts, then a coin, then a ten-sided die?
  17. How many outcomes are there from a card drawn from 52, then a coin, then a four-sided die?
  18. How many outcomes are there from a four-sided die, then a spinner with 8 equal parts?
  19. How many outcomes are there from a coin, then a ten-sided die, then a card drawn from 52?
  20. How many outcomes are there from a coin, then a six-sided die?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Counting PrincipleAnswer keyVersion 1

Date Period

Answer each question.

  1. How many outcomes are there from a spinner with 5 equal parts, then a card drawn from 52, then a ten-sided die?2600
  2. How many outcomes are there from a ten-sided die, then a four-sided die?40
  3. How many outcomes are there from a spinner with 5 equal parts, then a coin, then a spinner with 8 equal parts?80
  4. How many outcomes are there from a spinner with 5 equal parts, then a coin?10
  5. How many outcomes are there from a four-sided die, then a six-sided die?24
  6. How many outcomes are there from a spinner with 8 equal parts, then a ten-sided die?80
  7. How many outcomes are there from a spinner with 8 equal parts, then a spinner with 5 equal parts?40
  8. How many outcomes are there from a ten-sided die, then a four-sided die, then a spinner with 8 equal parts?320
  9. How many outcomes are there from a ten-sided die, then a coin, then a four-sided die?80
  10. How many outcomes are there from a six-sided die, then a ten-sided die?60
  11. How many outcomes are there from a six-sided die, then a coin, then a ten-sided die?120
  12. How many outcomes are there from a card drawn from 52, then a spinner with 8 equal parts, then a four-sided die?1664
  13. How many outcomes are there from a card drawn from 52, then a ten-sided die?520
  14. How many outcomes are there from a ten-sided die, then a card drawn from 52, then a coin?1040
  15. How many outcomes are there from a four-sided die, then a card drawn from 52?208
  16. How many outcomes are there from a spinner with 8 equal parts, then a coin, then a ten-sided die?160
  17. How many outcomes are there from a card drawn from 52, then a coin, then a four-sided die?416
  18. How many outcomes are there from a four-sided die, then a spinner with 8 equal parts?32
  19. How many outcomes are there from a coin, then a ten-sided die, then a card drawn from 52?1040
  20. How many outcomes are there from a coin, then a six-sided die?12

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

How many outcomes are there from a coin, then a six-sided die?

  1. The coin has 2 outcomes and the die has 6.
  2. Multiply them.

The answer is 12.

Where students go wrong

Adding instead of multiplying. Two outcomes then six outcomes is twelve, not eight, because every one of the two pairs with every one of the six.

Also called fundamental counting principle, sample spaces or multiplication principle.

Questions about these worksheets

Yes. Every counting principle sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the counting principle questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Adding instead of multiplying. Two outcomes then six outcomes is twelve, not eight, because every one of the two pairs with every one of the six.