GRE Quantitative Reasoning
The GRE Quantitative Reasoning section assesses your ability to understand, interpret, and analyze quantitative information, as well as to solve problems using mathematical concepts.
Probability and Combinatorics
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: \( C(n, r) = \frac{n!}{r!(n - r)!} \)
Key Formula
\[C(n, r) = \frac{n!}{r!(n - r)!}\]
Examples
What is the probability of rolling a 6 on a fair die?
How many different ways can you arrange the letters in 'CAT'?
In a Nutshell
Probability and combinatorics help you predict outcomes and count possibilities.