Combinations

When order doesn’t matter

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ counts unordered selections.
• Ask "does order matter?" If not, divide out the orderings.
• $\binom{n}{2} = \frac{n(n-1)}{2}$ counts pairs.

Steps

1. Order or not?
2. n choose k
3. Lottery
4. Handshakes
5. Everyone meets everyone
6. Poker