What is nCr Formula?
nCr represents “n choose r,” a concept in combinatorics that calculates the number of ways to select a group of items from a larger set without considering the order of selection. It is denoted mathematically as:
nCr = n! / (r!(n – r)!)
Where,
- “n” is the total number of items in the set,
- “r” is the number of items to be chosen, and
- “!” denotes factorial, which is the product of all positive integers from 1 to the given number.
Note: nCr Formula is also called Combination Formula.
nCr Formula
nCr Formula is one of the countless formulas in the world of mathematics, which plays a pivotal role in solving problems and gaining a deeper understanding of the subject. nCr formula deals with combinations and as we know, Combinations are an integral part of combinatorics, the branch of mathematics that focuses on counting and arranging objects.
They are widely used in probability and statistics to calculate the possible outcomes of events. They also have many applications in real-life situations such as forming teams, choosing passwords, arranging books, etc. In this article, we will explore the nCr formula in detail, discussing its importance, and applications and providing clarity through solved problems.
Table of Content
- What is Combination?
- What is nCr Formula?
- Properties of nCr
- Derivation of nCr Formula
- nPr and nCr Formula