Applications of nCr Formula
There are various application of nCr formula are:
- Probability: In probability theory, nCr is used to calculate the probability of certain events. For example, in a lottery, you can use nCr to calculate the probability of winning by choosing the winning numbers out of the total number of possible combinations.
- Binomial Coefficients: nCr appears in the binomial coefficient formula, which is used to expand binomial expressions. For example, in (a + b)n, the coefficients of each term can be calculated using nCr.
- Counting Subsets: You can use nCr to count the number of distinct subsets of a set with n elements. For instance, if you have a set of 5 elements, 5C0, 5C1, 5C2, 5C3, 5C4, and 5C5 represent the number of subsets with 0, 1, 2, 3, 4, and 5 elements, respectively.
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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