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The counting rule

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

How many possibilities are there? You can count them with a tree diagram (das Baumdiagramm). The counting rule (die Zählregel) is faster.
📄 Open worksheet (PDF, German)

The video

In the video Mira combines T-shirts and trousers, and three children line up in a row.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:16 The tree diagram
  3. 0:32 The counting rule
  4. 0:49 Orders
  5. 1:11 Careful, mistake!
  6. 1:28 Try it yourself

The most important points

\(3\) T-shirts and \(2\) pairs of trousers: in the tree diagram each T-shirt has \(2\) branches. At the end there are \(6\) paths.

The tree diagram with 6 combinations.
The tree diagram with \(6\) combinations.

Counting rule

Multiply the numbers of possibilities at each stage: \(3 \cdot 2 = 6\). With \(4\) caps: \(3 \cdot 2 \cdot 4 = 24\).

3 · 2 = 6.
\(3 \cdot 2 = 6\).

Orders: for place \(1\) there are \(3\) children, for place \(2\) still \(2\), for place \(3\) only \(1\): \(3 \cdot 2 \cdot 1 = 6\).

ABC, ACB, BAC, BCA, CAB, CBA.
ABC, ACB, BAC, BCA, CAB, CBA.

Careful: do not add! \(3 + 2 = 5\) is wrong: every T-shirt goes with every pair of trousers.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
Page 1/5
The worksheet – Page 2
Page 2/5
The worksheet – Page 3
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The worksheet – Page 4
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Show the worksheet solutions
The worksheet – Page 5
Page 5/5

Try it yourself

Task

Ice cream shop: \(4\) flavours, cone or cup, \(3\) sauces. One scoop, one sauce. How many possibilities are there?

Show solution

\(4 \cdot 2 \cdot 3 = 24\) possibilities.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Zählregel (Baumdiagramm, Möglichkeiten multiplizieren, Reihenfolgen). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.