Combinatorics
Definition
Combinatorics is the branch of mathematics dealing with the study of finite or countable discrete structures. It involves counting, arranging, and finding patterns in sets of elements.
5 Must Know Facts For Your Next Test
- The Multiplication Rule for Counting states that if one event can occur in 'm' ways and a second can occur independently of the first in 'n' ways, then the two events can occur in 'm x n' ways.
- Factorials are frequently used in combinatorics to determine the number of ways to arrange a set of objects.
- Permutations are specific arrangements of objects where order matters.
- Combinations are selections of objects where order does not matter.
- The binomial coefficient, often read as 'n choose k', represents the number of ways to choose 'k' elements from a set of 'n' elements without regard to order.
Review Questions
- What is the Multiplication Rule for Counting and how is it applied?
- How do permutations differ from combinations?
- What is a factorial and how is it used in combinatorics?
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Related terms
Factorial (n!): The product of all positive integers up to 'n', used in counting arrangements.
Permutation: An arrangement or ordering of a set where the order matters.
Combination: A selection from a set where order does not matter.
