Derivation of nPr Formula
Let the n different objects be a1, a2, a3, . . . , an.
- First place can be filled up by any one of the n objects in n ways.
- Second place can be filled up by any one of the remaining (n-1) objects in (n-1) ways.
- Third place can be filled up by any one of the remaining (n-2) objects in (n-2) ways.
This continues and goes on till the rth place is filled.
Number of ways of filling up the rth place = n-r+1
Total permutations (nPr) = n × (n – 1) × (n – 2) × … × (n – r + 1) = (n!)/(n-r)!
This formula calculates the number of ways to arrange ‘r’ elements out of ‘n’ distinct elements without repetition.
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