Stars & Bars

Sharing things out

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $n$ identical items among $k$ people: $\binom{n+k-1}{k-1}$.
• For “at least one each”, give one to everyone first.
• Many counting problems become “arrange some symbols in a row”.

Steps

1. Sweets
2. Stars and bars
3. At least one each
4. Ice-cream scoops
5. When does it apply?
6. Place the bars
7. Dice sums