Permutation Formula

About Permutation Formula

The permutation is a set of things arranged in a specific sequence. Set members or elements are placed in a sequential or linear order here. For instance, the permutation of set A=1,6 equals 2, as in 1,6 and 6,1. There are no alternative ways to arrange the items in set A, as you can see.

The elements in permutation must be organised in a specific sequence, whereas the order of the elements in a combination is irrelevant.

When we look at train, bus, and aeroplane timetables, we are left wondering how they are planned for the public's convenience. Of course, the permutation is quite useful in planning the departure and arrival timetables for these. Also, when we come across automobile licence plates with only a few alphabets and numerals. Permutations make it simple to create these scripts.

nPr = n!/(n-r)!

Definition of Permutation

Basically A permutation is a method of arranging objects in a specific order. When dealing with permutation, one must think about both selection and layout. In a nutshell, ordering is critical in permutations. To put it another way, a permutation is an ordered combination.

Formula

The formula for permutation of n objects for r object selection is as follows:P(n,r) = n!/(n-r)!

Solved Example of Permutation Formula

Example: The number of ways that 10 members can be awarded 3rd and 4th place is given by:

P(10, 2) = 10!/(10-2)! = 10!/8! = (10.9.8!)/8! = 10 x 9 = 90

Types of Permutation

Permutation can be classified into three different categories:

  1. Permutation of n different objects (when repetition is not allowed)
  2. Repetition, where repetition is allowed
  3. Permutation when objects are not distinct (Permutation of multisets)

Permutation of n different objects

P(n, r) indicates the number of all conceivable arrangements or permutations of n unique items taken r at a time if n is a positive integer and r is a whole number, such that r n. When using permutation without repetition, the number of options available decreases over time. It can also be written like this.

  • P(n, r) = n(n-1)(n-2)(n-3)……..upto r factors
  • P(n, r) = n(n-1)(n-2)(n-3)……..(n – r +1)

Here, “nPr” indicates the "n" things to be chosen without repetition from "r" objects, where the order matters.

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