PERMUTATION

Definition Of Permutation

Permutation is an ordered arrangement of a group of objects.

More About Permutation

The permutation of n objects taken r at a time is represented as nPr. 
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

Video Examples: Permutation and Combination

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.

Solved Example on Permutation

Ques: 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.