COUNTING & PROBABILITY

What Counting & Probability mean on the AMC10

This section is about counting carefully without double-counting and translating word problems into probability expressions. Key tools:

• Counting principles — addition, multiplication, complementary counting
• Permutations and combinations — $P(n,r)$ and $\binom{n}{r}$
• The pigeonhole principle — "with $k$ pigeonholes and $k+1$ pigeons..."
• Probability basics — favorable / total, independence, conditional
• Expected value — weighted averages of outcomes
• Geometric probability — area- or length-based probability

When stuck, try complementary counting ("what's the probability it does not happen") — it cuts many problems in half.