nPr and nCr Formula
Combination means selection. Here, the order does not matter. Whereas permutation of n different objects taken r at a time = (number of ways of selecting r objects from n different objects) *× (number of ways of arranging the selected r objects) i.e., permutation is the way to arrange some objects.
|
Formula |
Interpretation |
Expression |
|---|---|---|
|
nPr |
Permutation of ‘n’ different objects taken ‘r’ at a time |
n!/(n-r)! |
|
nCr |
Combination of n different objects taken r at a time |
n!/(n-r)!(r!) |
Where,
- n is the total number of objects,
- r is the number of objects taken at a time, and
- Factorial i.e., n! is the product of all positive integers from 1 to “n.”
Relationship between nPr and nCr Formula
As nPr = (number of ways of selecting r objects from n different objects) × r!
⇒ (number of ways of selecting r objects from n different objects) = nPr /r!
⇒ nCr = nPr /r! = n!/(n-r)!(r!)
Thus, the relationship between nPr and nCr Formula is:
nCr = nPr /r!
nPr Formula
nPr formula is used to find the number of ways in which r different things can be selected and arranged out of n different things. The nPr formula is, P(n, r) = n! / (n−r)!, and is also called Permutation Formula.
In this article, we learn about nPr formula, its significance, properties, mathematical derivation, and diverse applications across mathematics and real-world scenarios.
Table of Content
- What is nPr Formula?
- Properties of nPr Formula
- Derivation of nPr Formula
- nPr and nCr Formula
- Applications of Permutation (nPr) Formula
- Examples on nPr Formula
- Practice Problems on nPr Formula
- nPr Formula: FAQs