What is Combination in Maths?
Combination is the choice of selecting r things from a group of n things without replacement and where the order of selection is not important.
Number of combinations when ‘r’ elements are selected out of a complete set of ‘n’ elements is denoted by nCr
nCr = n! / [(r !) × (n – r)!]
Example: Let n = 4 (E, F, G, H) and r = 2 (consisting of all the combinations of size 2).
nCr = 4C2
= 4!/((4-2)!×2!)
= 4×3×2×1 / 2×1×2×1 = 6
The six combinations are EF, EG, EH, FG, FH, and GH.
Combinations Meaning
Combinations refer to a way of selecting items from a larger set such that the order of selection does not matter.
Combinations
Combination is a way of choosing items from a set, such as (unlike permutations) the order of selection doesn’t matter. In smaller cases, it’s possible to count the number of combinations. Combination refers to the mixture of n things taken k at a time without repetition. To know the combinations in the case where repetition is allowed, terms like k-selection or k-combination along with repetition are often used.
Combinations are particularly useful in scenarios where the outcome depends on the presence or absence of items rather than their sequence, making them a fundamental tool in various probability and statistical analyses, as well as in everyday decision-making processes that involve selecting subsets from a larger set.
In this article, we will learn about combinations in detail, along with their formulas, how to calculate combinations, etc.
Table of Content
- What is Combination in Maths?
- Basic Principles of Counting
- Combination Formula
- Permutations and Combinations
- How to Calculate Probability of Combinations?
- What is Handshaking Problem?
- Handshaking Combination
- Examples on Combinations
- Combinations Class 11
- Practice Problems on Combinations