nPr Formula: FAQs

What are Permutations?

Permutations are arrangements of objects in a specific order. In mathematics, particularly in combinatorics, a permutation of a set is an ordered arrangement of its distinct elements.

What is nPr Formula in Probability?

The nPr formula is:

nPr = n! / (n – r)!

What is the Value of nP0?

nP0 is defined as 1. In combinatorics, the number of ways to arrange 0 elements (which essentially means having an empty set) is considered to be 1.

What is the Meaning of r in nPr?

In nPr, r is the number of objects chosen and arranged from the total n objects.

How do you know when to use nCr or nPr?

We use nPr when order of arrangement matters, whereas we use nCr when it doesn’t.

Is nPr always greater than nCr?

No, nPr is not always greater than nCr for same value of r and n.

What is the nPr and nCr formula?

The nPr and nCr formula are:

  • nPr = n! / (n – r)!
  • nCr = = n! / r! × (n – 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

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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?...