Enhance Your Learning with Permutations and Combinations Flash Cards for quick learning
An arrangement of objects in a specific order.
A selection of objects without considering the order.
The product of all positive integers less than or equal to a given positive integer.
The formula to calculate the number of permutations of n objects taken r at a time: P(n, r) = n! / (n - r)!
The formula to calculate the number of combinations of n objects taken r at a time: C(n, r) = n! / (r! * (n - r)!)
A principle that states that if there are m ways to do one thing and n ways to do another, then there are m * n ways to do both.
Permutations where some elements are repeated.
Combinations where some elements are repeated.
Permutations of sets with repeated elements.
Combinations of sets with repeated elements.
Using permutations to calculate probabilities.
Using combinations to calculate probabilities.
Permutations where the order matters but the starting point is fixed.
Permutations where no element appears in its original position.
A principle that states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.
The coefficient of a term in the expansion of a binomial raised to a positive integer power.
A triangular array of numbers where each number is the sum of the two numbers directly above it.
A method used to count the number of ways to distribute identical objects into distinct groups.
A principle used to count the number of elements in the union of multiple sets.
A way to represent a sequence of numbers as a power series.
Numbers that arise in combinatorial mathematics and calculus.
Numbers that arise in various counting problems.
A lemma used to count the number of distinct colorings of a mathematical object under a group of symmetries.
A theorem used to count the number of distinct colorings of a mathematical object under a group of symmetries.
Arrangements of objects that satisfy certain conditions.
A square grid filled with symbols, each occurring exactly once in each row and column.
A set of subsets of a given set, each of the same size, such that each element of the given set is contained in the same number of subsets.
The study of mathematical structures used to model pairwise relations between objects.
A cycle in a graph that visits each vertex exactly once.
A cycle in a graph that visits each edge exactly once.
A graph that can be drawn on a plane without any edges crossing.
The minimum number of colors needed to color the vertices of a graph so that no two adjacent vertices have the same color.
The minimum number of vertices in a graph such that every possible edge coloring results in a certain property.
The process of finding the best solution from a finite set of possible solutions.
A problem in which a salesman needs to find the shortest possible route that visits each city exactly once and returns to the starting city.
A problem in which a set of items with certain values and weights must be selected to maximize the total value while keeping the total weight below a certain limit.
A problem in which the vertices of a graph must be colored using a minimum number of colors so that no two adjacent vertices have the same color.
The study of mathematical games with perfect information and no chance elements.
A two-player mathematical game in which players take turns removing objects from distinct piles.
A theorem that assigns a nimber to each position in a combinatorial game, determining its outcome.
The study of geometric arrangements of objects, often involving counting and optimization problems.
The smallest convex polygon that contains all the given points.
A partitioning of a plane into regions based on the distance to a specified set of points.
A technique used in drug discovery and materials science to rapidly synthesize and screen large numbers of chemical compounds.
An auction in which bidders can place bids on combinations of items rather than just individual items.
A phenomenon in which the number of possible combinations or permutations grows rapidly as the size of the problem increases.
A proof that uses combinatorial arguments to establish the truth of a mathematical statement.
An equation that relates different combinatorial quantities.
A problem in which the goal is to find the best solution from a finite set of possible solutions.
A digital circuit that performs combinatorial logic operations.