Permutations and Combinations
Concept Overview
- Permutations: Arrangements where the order of items matters.
- Combinations: Selections where the order does not matter.
- Core Idea: Counting possibilities systematically to avoid repetition or omission.
Real-Life Analogies
- Permutations: Seating arrangements, lock codes, or password generation.
- Combinations: Lottery draws, team selection, or forming committees.
Applications
- Used in probability to calculate chances of different outcomes.
- In statistics, they help in sampling and data organization.
- In computer science, they are used in coding, optimization, and algorithm design.
Series Formulas | Arithmetic, Geometric, Power, Fourier & More
Probability Formulas
Concept of Probability
Probability measures the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
Understanding Events
- Simple Event: One specific outcome (e.g., rolling a 4 on a die).
- Compound Event: Combination of multiple outcomes.
- Complementary Event: The opposite of an event happening.
- Independent Events: Outcomes not affecting each other (e.g., tossing two coins).
- Mutually Exclusive Events: Events that cannot occur together (e.g., drawing a red card and a black card in the same draw).
Real-Life Examples
- Tossing a coin: Heads or tails.
- Drawing cards: Probability of getting an ace.
- Weather predictions: Chance of rain based on data.
- Risk analysis: Insurance and financial modeling.
Applications
- Data Science: Predictive modeling and machine learning.
- Insurance and Finance: Risk assessment and premium calculation.
- Gaming: Understanding chances in lotteries, board games, or casinos.
- Daily Life: Decision-making under uncertainty.
