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
.
- The permutation or arrangement of 9 different balls in 3 different rows can be done in
= 504 ways.
- The permutation of n objects taken all at a time is represented as
.
- 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 
= 7! = 5,040. [
= 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
Additional Links for Permutation
