What is nPr Formula?

A permutation is an arrangement of all or part of a set of objects, about the order of the arrangement. The nPr formula is used to calculate the number of permutations of n distinct objects taken r at a time. It is denoted mathematically as:

nPr = n! / (r!(n – r)!)

where,

  • n” is the total number of items in the set,
  • r” is the number of items to be chosen, and
  • !” denotes factorial, which is the product of all positive integers from 1 to the given number.

nPr Formula

nPr formula is used when we have to choose “r” options out of “n” choices. And the nPr formula is,

P (n, r) = nPr = nPr = n! / (n – r)!

Where,

  • n is Total Number of Things
  • r is Number of Things that have to be Selected and Arranged

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

Similar Reads

What is nPr Formula?

A permutation is an arrangement of all or part of a set of objects, about the order of the arrangement. The nPr formula is used to calculate the number of permutations of n distinct objects taken r at a time. It is denoted mathematically as:...

Properties of nPr Formula

Some of the common properties of the nPr Formula are:...

Derivation of nPr Formula

Let the n different objects be a1, a2, a3, . . . , an....

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....

Applications of Permutation (nPr) Formula

Various applications of nPr Formula are:...

Examples on nPr Formula

Example 1: Suppose you have a deck of 52 playing cards, and you want to find the number of ways to choose 5 cards in a specific order from the deck (i.e., permutations of 5 cards out of 52)....

Practice Problems on nPr Formula

P1. If 2n+1Pn-1:2n-1Pn = 3:5, then find the value of n....

nPr Formula: FAQs

What are Permutations?...