This document defines and provides examples of permutation, including linear permutation without repetition, permutation with repetition, distinguishable permutation, and circular permutation. It gives the formula to calculate circular permutation as (n-1)!, where n is the total number of objects. Examples show using the formula to find the number of ways to arrange people around a circular table or cheerleaders in a circular pattern. An activity asks the reader to use the formula to calculate the number of arrangements for knights around a round table and swimmers in a circular pattern.

1. PERMUTATION
Eddie A. Lumaras, Jr.

2. PERMUTATION
Definition
A permutation is an arrangement of objects in a definite
order. Also, it is a mathematical technique that determines
the possible arrangements in a set when the order of
arrangements matters.

3. TYPES OF PERMUTATION
1. Permutation without Repetition (Linear Permutation)
2. Permutation with Repetition or Replacements
3. Distinguishable Permutation
4. Circular Permutation

4. ASSIGNMENTS

5. REVIEW:
Find the number of distinguishable permutations of the letters in each of the
given words.
1. REFERENCE
2. STATISTICS

6. CIRCULAR PERMUTATION
The number of circular permutation of n objects is given by
P = (n-1)!
Where:
P is the total number of permutations
n is the total number of objects in the set

7. EXAMPLES:
Solve:
1. Find the number of permutation of five people around a circular table.
Formula:
P = (n-1)!
Given:
P = ?
n = 5
Solution:
P = (n-1)!
P = (5-1)!
P = 4!
P = 24 ways

8. EXAMPLES:
2. Find the number of circular permutation of seven cheerleaders.
Formula:
P = (n-1)!
Given:
P = ?
n = 7
Solution:
P = (n-1)!
P = (7-1)!
P = 6!
P = 720 ways

9. ACTIVITY:

10. DIRECTIONS: SOLVE THE FOLLOWING PERMUTATIONS
1. In how many ways can King Arthur arrange 8 knights around
a round table?
2. In how many ways can the 10 swimmers on an aquatic ballet
team be arranged in a circular pattern?