The document discusses various types of permutations including distinguishable, circular, and permutations taken r at a time, and provides formulas for calculating the number of arrangements. It includes examples and exercises related to these permutations, such as arranging letters from specific words and the seating arrangements of people or objects. The exercises require the application of permutation principles to solve practical problems involving the arrangement of items.

1. Other types of Permutation
•Taken r at a time
•Distinguishable Permutation
•Circular Permutation

2. PERMUTATION
A permutation is an arrangement of things in a
definite order or the order of arrangement of
distinguishable objects without allowing
repetitions among the objects.
 LINEAR PERMUTATION
 PERMUTATION TAKEN R AT A TIME
 INDISTINGUISHABLE PERMUTATION
 CIRCULAR PERMUTATION

3. EVALUATE THE FOLLOWING:
1.4 x 3 x 2 x 1
2.5 x 4 x 3 x 2 x 1
3.6!
4.3!
5.(8 – 1)!
24
120
720
6
5,040

4. PERMUTATION OF
OBJECTS
TAKEN R AT A TIME

5. The number of permutations of
r members of a set containing
n different element is given by:
nPr=

6. EXAMPLES
In how many ways can letters in the word PALINDROME be arranged using:
a. 3 letters at a time?
b. 5 letters at a time?
c. 6 letters at a time?
d. all letters?

7. SEATWORK 3.3Find the number of
permutation
1. In a certain general assembly, four major prizes
are at stake. In how many ways can the first,
second, third and fourth prizes be drawn from a
box containing 12 names?
2. In how many different ways can 5 bicycles be
parked if there are 7 available parking spaces?
3. In how many ways can aling Rosa arrange 7
potted plants if there are 10 pots to choose from?

8. 4. In a certain general assembly, four
major prizes are at stake. In how many
ways can the first, second, third and
fourth prizes be drawn from a box
containing 12 names?
5. In how many ways can aling Rosa
arrange 7 potted plants if there are 10
pots to choose from?

9. DISTINGUISHABLE
PERMUTATION

10. The number of Distinguishable
Permutation P of n object taken
n at a time with r1 like element, r2
like element and so on is given
the formula

11. Examples;
Find the number of permutation
of the following problems.
1. How many distinguishable
permutation are possible with all the
letters of the word ALGEBRA?

12. 2. Find the number of
distinguishable
permutation of the word
PEPPER.

13. 3. How many distinguishable
permutation are possible
with all the letters of the
word STATISTICS?

14. SEATWORK 3.4
FIND THE NUMBER OF DISTINGUISHABLE
PERMUTATION FOR THE FF WORDS
1.EXCITEMENT
2.EXTRAVAGANT
3.INDUSTRIOUS

15. CIRCULAR
PERMUTATION
Pc=

16. 1. Four friends dine in a Chinese
Restaurant, and they will be seated at a
round table. In how many ways they
can be seated?
2. Find the number of ways to choose of
5 different books from a bookshelf of
15 books.
EXAMPLES;

17. SEATWORK 3.5
FIND THE NUMBER OF PERMUTATION
1. 6 students are need to be lined – up for a
picture taking, if 3 of them insist that they
should be need to be each other. In how
many ways can you arrange them?
2. If there are 8 people and only 3 chairs are
available, in how many ways can they be
seated?

18. 4. In how many ways can 6 knights be
seated in 6 chairs around a round table?
5. Find the distinguishable permutation of
the ff words.
a. MEASUREMENT b. MISSISSIPPI
c. COMMISSIONER