The document discusses the fundamental principle of counting, explaining how to determine the total number of ways events can occur using permutations and combinations. It provides various examples to illustrate the concepts of arrangements, including distinguishable permutations and circular permutations. Additionally, it emphasizes the significance of order in permutations while asserting that order does not matter in combinations.

1. PERMUTATION
PREPARED BY: JEORGE O. HUGNO

2. FUNDAMENTAL PRINCIPLE OF COUNTING
•It states that in a sequence of events, the total
number of possible ways all events can be
performed is the product of the possible number
of ways each individual event can be performed.

3. TWO WAYSTO ENUMERATE ALLTHE POSSIBLE OUTCOMES
• Table
• Systematic Listing
• Tree Diagram

4. EXAMPLE NO. 1
•If you have three different T-shirts, two pair of
shorts, and two pairs slippers, how many outfits
composed of a T-shirts, a pair of shorts, and a pair
of slippers would you have?

5. EXAMPLE NO. 2
•A die and a coin are tossed once. How many
possible outcomes are there?

6. EXAMPLE NO. 3
•How many ways can you assemble mountain
bike with four kinds of frames and two kinds of
handle bars?

7. PERMUTATION
•It is an arrangement of things in a definite order
or the ordered arrangement of distinguishable
objects without repetition among the objects.

8. FORMULA
• The number of permutations of n things taken n at a time:
nPn = n!
• The number of permutations of n things taken r at a time:
nPr =

9. EXAMPLE NO. 1
• You want to arrange four paintings in a row along your
hallway. In how many ways can you arrange the
paintings?

10. EXAMPLE NO. 2
• Find the number of ways a sari-sari store owner can
arrange 8 different can goods.

11. EXAMPLE NO. 3
• Two raffle tickets will be drawn from 30 raffle tickets
for the grand prize and a consolation prize. In how
many ways can teo raffle tickets be drawn from the 30
raffle tickets?

12. EXAMPLE NO. 4
• How many five-letter words can you make from the
letter of the word BIRTHDAY?

13. EXAMPLE NO. 5
• How many five-letter words can you make from the
letter of the word BIRTHDAY?

14. EXAMPLE NO. 6
• Find the number of distinguishable permutations of the
letters in the word BASKETBALL?

15. DISTINGUISHABLE PERMUTATION
• It refers to the permutation of a set of objects where
some of them are alike.
P =

16. EXAMPLE NO. 6
• Find the number of distinguishable permutations of the
letters in the word BASKETBALL?

17. EXAMPLE NO. 7
• In how many ways can the word PROBABILITY be
arranged?

18. EXAMPLE NO. 8
• In how many ways can 5 person be seated in a circular
table?

19. CIRCULAR PERMUTATION
• It is the possible arrangement of objects in a circle.
P = (n-1)!

20. EXAMPLE NO. 8
• In how many ways can 5 person be seated in a circular
table?

21. EXAMPLE NO. 9
• In how many ways can 12 persons be seated in a round
table with 12 chairs?

22. COMBINATION

23. BASKETBALL & COMBINATION
•The Jackson Wildcats play basketball in a highly
competitive city district.There are 8 teams in the
district and they all play each other once during
the season.The coach wants to know how many
games will be played in the district this season.

24. COMBINATION
•It is an arrangement of objects in which the
order is not important.
nCr =

25. BASKETBALL & COMBINATION
•The Jackson Wildcats play basketball in a highly
competitive city district.There are 8 teams in the
district and they all play each other once during
the season.The coach wants to know how many
games will be played in the district this season.

26. SAMPLE SITUATIONS OF COMBINATION
•Five badminton players chosen from a group of
nine.
•Selecting 5 problems in a 10-item Mathematics
problem-solving test.

27. EXAMPLE NO. 1
• In how many ways can a committee consisting of 4
members be formed from 8 people?

28. EXAMPLE NO. 2
• How many ways can 5 books be selected from 9 books,
if the order of the selected book doesn’t matter.

29. EXAMPLE NO. 3
• A basket contains 4 star apples, 5 mangoes and 8
guavas. How many ways can 2 star apples, 1 mango and
2 guavas be chose?