Advanced Topics
In a nutshell: Probability and combinatorics help you predict outcomes and count possibilities.
## 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: \( C(n, r) = \frac{n!}{r!(n - r)!} \)
C(n, r) = \frac{n!}{r!(n - r)!}
Examples
- What is the probability of rolling a 6 on a fair die?
- How many different ways can you arrange the letters in 'CAT'?