Properties of nCr
Some of the common properties of nCr are:
- nCr is the same as nCn-r, which means that choosing r items out of n items is equivalent to choosing (n-r) items out of n items.
- nCr is a natural number, which means that it is always a positive integer. For example, 4C2 is 6, which is a natural number.
- nCr follows the binomial theorem, which means that it can be used to find the coefficients of the expansion of (x + y)n. For example, the coefficients of (x + y)4 are 4C0, 4C1, 4C2, 4C3, and 4C4, which are 1, 4, 6, 4, and 1 respectively.
- nC1 = n, which means there are ‘n’ ways of choosing one object from ‘n’ objects.
- nCx = nCy implies either x = y or x + y = n, which means the number of ways of choosing x objects from n objects is equal to the number of ways of choosing y objects from n objects only if x and y are equal or complementary (sum up to n).
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