Understanding Chances and Counting Methods

Probability and combinatorics questions test your ability to calculate the likelihood of events and count possible outcomes.

Key Ideas

• Probability basics: \( \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \)
• Counting principles: the fundamental counting principle, permutations, and combinations.

Where It’s Useful

Making decisions with uncertainty (like picking teams), or understanding odds in games, relies on these concepts.

GRE Applications

• "At least" and "at most" scenarios.
• Multi-step events (like picking two cards in a row).

Formula

The number of combinations of \( n \) items taken \( r \) at a time: \( C(n, r) = \frac{n!}{r!(n - r)!} \)