TwiddleLab / Math / Counting and Patterns

Choices Multiply

Lesson 1 of 11 · 5 min · Free, no account needed

What you will learn

• When choices are made one after another and do not limit each other, multiply the number of options.
• A tree of choices shows why: every branch splits again, and the leaves are all the outcomes.
• 3 shirts, 4 pants and 2 pairs of sneakers make 3 × 4 × 2 = 24 outfits.

Start the lesson

How the lesson goes

1. 3 shirts, 4 pants, 2 pairs of sneakers.

   How many different outfits can you wear to school? Drag the lever to your bet.

2. Start small: 3 shirts and 2 pants. Find every outfit.

   Tap a shirt and a pair of pants. Each new outfit lights its square.

3. Now the full wardrobe, as a tree.

   Grow one level at a time and watch the leaves.

4. This is the counting principle.

   Make one choice, then another, then another. If no choice limits the others, every branch splits the same way.

   So the number of outcomes is the product: 3 × 4 × 2 = 24.

   This is the counting principle (also called the rule of product). Multiply, don't list.

5. Design your cafe menu: exactly 24 different lunches.

   A lunch is one main, one side and one drink. Offer at least 2 of each.

   Each lunch is a path main, side, drink through the tree, so the count is the product of the three group sizes.

6. Game: quick count. Four pictures, no lists allowed.

   Tap the right count under each picture. Fewer misses, more stars.

7. Independent choices multiply.

   Your menu is open. Take three orders.

Next lesson: Arrangements: Factorials as Trees · Part of the course: Counting and Patterns

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