Arrangements

Permutations and factorials

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

• $n!$ ways to arrange $n$ distinct items in a row.
• Arranging $k$ of $n$: $\frac{n!}{(n-k)!}$.
• Divide by the factorials of repeated items.

Steps

1. Line them up
2. Factorials
3. Podium
4. Stuck together
5. Round the table
6. A million seatings
7. Repeated letters