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Linear Permutation Calculator

Type:
nPn
 =
3P3
 =
Answer: Ways to arrange 3 elements in a row is 6.
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Linear Permutation Selector 𝒊
A➔B➔C[#1]
A➔C➔B[#2]
B➔A➔C[#3]
B➔C➔A[#4]
C➔A➔B[#5]
C➔B➔A[#6]
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Linear Permutation

Permutation is a mathematical concept that refers to the arrangement of elements from a collection, where the order in which the elements are chosen affects the result. Linear permutations involve arranging elements in a straight line, with each arrangement being unique based on the order of the elements. Even a slight change in the position of an element can lead to a different arrangement.
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Linear Permutation Formula

In cases where we want to arrange people or elements in a straight line, we can determine the number of possible arrangements using the linear permutation Formula:
n P n = n !
nPn = Permutation of n distinct elements | n = total number of elements

Linear Permutation Examples

Explore the following Linear Permutation examples to understand how to calculate arrangements in various scenarios.
Example 1: Permutations of Students in a Row
  • Problem: How many ways can 4 students (A, B, C, D) be arranged in a row for a photograph?
  • Solution: There are 4 students, so there are 4! = 4 × 3 × 2 × 1 = 24.
  • Answer: There are 24 ways to arrange them.
Example 2: Permutations of Letters in a Word
  • Problem: How many ways can the letters in the word CAT be arranged?
  • Solution: There are 3 letters, so there are 3! = 3 × 2 × 1 = 6.
  • Answer: There are 6 ways to arrange the letters.
Example 3: Permutations of Players in a Team
  • Problem: How many ways can 6 players be lined up for a team photo?
  • Solution: There are 6 players, so there are 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
  • Answer: There are 720 ways to arrange the players.

Linear Permutation Exercise

Engage in this Linear Permutation exercise to explore the concept of permutations through practical questions. Test your ability to calculate arrangements.
Que 1: How many ways can 5 students be seated in a row?
Ans 1: 120.
Que 2: How many ways can 4 different colored balls be arranged in a straight line?
Ans 2: 24.
Que 3: How many ways can 6 different books be placed on a shelf?
Ans 3: 720.
Que 4: How many ways can 3 letters (A, B, C) be arranged in different orders?
Ans 4: 6.
Que 5: How many ways can 7 people stand in a line for a photo?
Ans 5: 5040.

Linear Permutation Calculator FAQ

In what situations should I use linear permutations?
Linear permutations are used when arranging objects in a specific order, such as arranging students in a line for a performance, arranging books on a shelf, or arranging items in a queue.
What is a permutation with restriction in linear arrangements?
A permutation with restriction involves additional conditions, such as certain objects needing to be next to each other or not next to each other. These conditions modify the calculation of arrangements.
What happens if no elements are selected (r = 0) in a linear permutation?
If no elements are selected, there is exactly 1 possible arrangement—the empty arrangement, where nothing is chosen or arranged.
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