nPr and nCr Formula
The nPr and nCr formulas are used to calculate the number of ways to arrange or select objects from a given set of objects. The difference between them is that nPr considers the order of the objects, while nCr does not.
| Formula | Interpretation | Formula Expression |
|---|---|---|
| nPr | Permutations of “n” objects taken “r” at a time. | nPr = n! / (n – r)! |
| nCr | Combinations of “n” objects taken “r” at a time. | nCr = n! / (r! × (n – r)!) |
Where,
- n is the total number of objects,
- r is number of objects taken at a time, and
- Factorial i.e., n! is the product of all positive integers from 1 to “n.”
- i.e., n! = n × (n – 1) × (n – 2) × . . . × 2 × 1
For example, if we have 3 letters A, B, and C, and we want to arrange them in different ways, we can use the nPr formula. Using the nPr formula we get the answer 6 for this arrangement. This means that there are 6 ways to arrange the 3 letters: ABC, ACB, BAC, BCA, CAB, and CBA.
However, if we want to select 2 letters out of the 3 letters, without caring about the order, we can use the nCr formula. Using the formula we get 3 as result, this means that there are 3 ways to select 2 letters out of the 3 letters: AB, AC, and BC.
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