This document discusses permutations and circular permutations. It begins with examples of finding the number of permutations and circular permutations of words. It then provides practice problems involving permutations of letters in words and arrangements of objects. The document emphasizes distinguishing between permutation problems involving distinguishable or identical objects, and using the appropriate formula to calculate permutations or circular permutations.

1. DISTINGUISHABLE
PERMUTATION AND
CIRCULAR PERMUTATION

2. 2 – MINUTE DRILL
BASIC FUNDAMENTAL OF
OPERATIONS

3. REVIEW!

4. HOW MANY “WORDS” CAN BE
FORMED USING ALL THE
LETTERS OF THE WORD:
A. SAD
B. MATH

5. MISSISSIPPI IS A STATE OF NORTH AMERICA. IT
BECAME PART OF THE US AFTER THE
REVOLUTIONARY WAR LATER PART OF 18TH
CENTURY.
• CAN YOU FIND THE NUMBER OF PERMUTATION FROM THE WORD
MISSISSIPPI?
• SUPPOSE YOU ARRANGE ALL THE LETTERS FROM THE WORD
MISSISSIPPI IN A CIRCULAR FORM, HOW MANY POSSIBLE
ARRANGEMENTS CAN YOU MAKE?
LATER PART OF THE LESSON YOU WILL KNOW THE ANSWER.
Mi . Suh. Si. Pee.

6. 1. Find the number of permutations of
the letters from the word STATISTICS.
2. In how many ways can 3 people be
seated around a circular table?
How do you find the answer?
Let us see …

7. Let us take the word STATISTICS
How many letters are there?
Assuming letters are distinct, what is its
permutation?
 What are the letters that are alike? How
many times it appear from the given word?
DISTINGUISHABLE
PERMUTATION

9. In how many ways can 3 people be
seated around a circular table?
CIRCULAR
PERMUTATION
The permutation of n objects arrange in
a circle is
P = (n-1)!

10. Will you now find the permutation of the word
MISSISSIPPI if it will arrange in circular
position?
CIRCULAR
PERMUTATION

11. Read carefully the permutation problem.
Problem 1. Five books in mathematics, three in Literature,
and two in Science are to be arranged on a shelf that has
space just enough for these ten books. Assuming that the
books in the same subject are identical, how many ways
can they be arranged?
Problem 2. A spinner is divided into 6 equal parts. In how
man ways can you arrange the four suits in the spinner?

12. Problem 3. In how many ways can 6 different-colored
horses be positioned in a carousel?
Problem 4. There are men in the chorus of an opera.
Half of them must wear long baggy pants, one-fourth
long straight pants, and the rest, short pants. How
many different ways may the pants be allocated to the
men?

13. How can we know that the given
situation is a problem on
distinguishable permutation?
Circular permutation?
What is the formula for
distinguishable permutation?
Circular permutation?

14. Decide what formula to be used in solving
the following problems.
1. Suppose an identical twin, identical triplets and
three other children pose for a photograph. How
many photographs will be different?
2In how many ways can 8 different-colored horses
be positioned in a carousel?

17. THANK YOU, GRADE
10!