Permutation
Definition of Permutation

• Permutation is an ordered arrangement of a group of objects.

Examples of Permutation

• Suppose Amy, Brian, and Charles are to sit side by side. Then there are 6 different orders in which they can arrange themselves.
  ABC, ACB, BAC, BCA, CAB, CBA – each of these permutation is different from the others.

More about Permutation

• The permutation of n objects taken r at a time is represented as _nP_r.
  
• The permutation or arrangement of 9 different balls in 3 different rows can be done in ₉P₃ = 504 ways.
• The permutation of n objects taken all at a time is represented as _nP_n = n!.
• Factorial: Factorial means a series of multiplications from 1 up to some number. An exclamatory symbol (!) indicates a factorial.
  For example, 3! means 3 × 2 × 1.
  7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 

Solved Example on Permutation

Find the number of 7-letter permutation from the letters of the word FORMULA.
Choices:
A. 5,040
B. 7
C. 1
D. 49
Correct Answer: A
Solution:
Step 1: The number of letters in the word FORMULA is 7.     [Write the number of letters of the word.]
Step 2: The number of 7-letter permutations from the 7 distinct letters of the word is ₇P₇ = 7! = 5,040.             [_nP_n = n!.]
Step 3: The number of 7 letter permutations from the 7 distinct letters of the word FORMULA is 5,040.

Related Terms for Permutation

• Linear Permutation

Additional Links for Permutation

• Click here for samples
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