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1 of 30
3x2x1=6
!
x4x3x2x1=120
5
5 =120
In Mathematics, factorial refers to the product of all
positive integers less than or equal to a particular
positive integer. It is usually denoted by that integer
and an exclamation point.
That is, n!= n x (n-1) x…x 1.
Factorial Notation
EXERCISE:
1. 3!
Ans: 6
EXERCISE:
2. 4!
Ans: 24
EXERCISE:
3. 4! + 3!
Ans: 30
EXERCISE:
4.
𝟔!
𝟒!
Ans: 30
EXERCISE:
5. (20-17)! =
Ans: 6
Special case of
Factorial Permutation
1! and 0! is always equal to 1.
PERMUTATION
is a mathematical technique
that determines the number
of possible arrangements in a
set when the order matters.
arrangements
order
Activity:
Identify which is illustrate a permutation.
Comment LIKE EMOJI if the order is Permutation and
comment HEART EMOJI if the orders is not permutation
1. Determining the top three winners
in mathematics Quiz Bee.
Activity:
2. Choosing five groupmates for your
Mathematics Project.
Activity:
3. Three people posing for
a picture.
Activity:
4. Assigning 4 practice
teachers to 4 different
grade levels
Activity:
5. Picking 2 questions from
a bowl.
The permutation of 𝑛 things or objects taken 𝑟 at
a time can be denoted in different ways:
𝑷 (𝒏, 𝒓) or 𝑛𝑃𝑟 or 𝑷(
𝑛
𝑟
)
Where:
n is the number of objects and
r is the number of how many objects will
be taken at a time.
Evaluate the following:
1. P(5,3)=
2. P(8,2)=
3.
𝑃 (6,2)∙𝑃(5,3
P(4,2)
=
4.
𝐏(𝟓,𝟐)∙𝐏(𝟑,𝟐)
𝐏(𝟒,𝟐)
=
120
56
150
10
Let’s solve problem involving permutation
1. There are 4 cyclists in a race. In how many
ways will they be ranked as first, second, and
third placers?
a. What is the value n?
b. what is the value r?
c. What is answer?
= 4
= 3
P(4,3)= 4x3x2 = 24
Let’s solve problem involving permutation
2. Arranging 4 different potted plants in a
row.
a. What is the value n?
b. what is the value r?
c. What is answer?
= 4
= 4
P(4,4)= 4x3x2x1
= 24
Let’s solve problem involving permutation
3. Electing a Mathematics club president,
vice-president and a secretary from 10
members.
a. What is the value n?
b. what is the value r?
c. What is answer?
= 10
= 3
P(10,3)= 10x9x8
= 720
Fundamental Counting Principle (FCP)
The Fundamental Counting Principle
(FCP) states that if one event has m
possible outcomes and a 2nd event
has n possible outcomes, then there
are m⋅n total possible outcomes for
the two events together.
(GROUP ACTIVITY)- Presenter, secretary, team leader
Cycling is good for health so many
workers choose to use bicycle
going to their workplace. Help the
5 workers reach their workplace
by crossing the right way going to
work.
Decode: Me! Solve the problem and write the matching letter on the blank
above the answer.
1) A-------- 0!
2) B-------- 4!+2!
3) K-------- P(6,2)
4) D-------- P(4,3)
5) I--------- P(7,2)
6) L-------- a horse race has 12 horses. How many different
ways can first, second and third occur?
7) M-------- 8!-7!
8) N-------- The number of photographs of 10 friends taken 3
at a time.
9) O-------- In how many ways can you arrange 5 math books
on a shelf?
10) S-------- P(3,3)
11) Y-------- 7!
What are the DepED Core Values?
What is Factorial Notation?
factorial refers to the product
of all positive integers less
than or equal to a particular
positive integer
What is a permutation?
refers to any one of all
possible arrangements of the
elements of the given set.
Quiz Time!
Directions: Choose the letter of the correct answer
_____________1) A ________ is an arrangement of things in a definite order or ordered
arrangement of objects.
S. permutation M. probability I. integration L. combination
_____________2) It is the product of all positive integers less that or equal to a particular positive
integers.
S. permutation M. Factorial Notation I. Probability E. Combination.
_____________3). Evaluate 4! - 3!
S. 16 M. 17 I. 18 L. 19
_____________4). Which of the following is equal to
6∙5∙4∙3∙2∙1
4∙3∙2∙1
?
S.
6!
3!
M.
6!
5!
E.
4!
6!
L.
6!
4!
_____________5. Ms. Cruz loves collecting plants. Suppose that she has 6 different potted plants
and she wishes to arrange 4 of them in a row, in how many ways can this be done?
E. 360 L. 720 I. 24 S. 1020
Agreement/ Assignment
Study the
Combination
SLM (mod 3)
Reference:
LM pages 285-290.

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permutation lesson.pptx

  • 1.
  • 4. In Mathematics, factorial refers to the product of all positive integers less than or equal to a particular positive integer. It is usually denoted by that integer and an exclamation point. That is, n!= n x (n-1) x…x 1. Factorial Notation
  • 7. EXERCISE: 3. 4! + 3! Ans: 30
  • 10. Special case of Factorial Permutation 1! and 0! is always equal to 1.
  • 11. PERMUTATION is a mathematical technique that determines the number of possible arrangements in a set when the order matters. arrangements order
  • 12. Activity: Identify which is illustrate a permutation. Comment LIKE EMOJI if the order is Permutation and comment HEART EMOJI if the orders is not permutation 1. Determining the top three winners in mathematics Quiz Bee.
  • 13. Activity: 2. Choosing five groupmates for your Mathematics Project.
  • 14. Activity: 3. Three people posing for a picture.
  • 15. Activity: 4. Assigning 4 practice teachers to 4 different grade levels
  • 16. Activity: 5. Picking 2 questions from a bowl.
  • 17. The permutation of 𝑛 things or objects taken 𝑟 at a time can be denoted in different ways: 𝑷 (𝒏, 𝒓) or 𝑛𝑃𝑟 or 𝑷( 𝑛 𝑟 ) Where: n is the number of objects and r is the number of how many objects will be taken at a time.
  • 18. Evaluate the following: 1. P(5,3)= 2. P(8,2)= 3. 𝑃 (6,2)∙𝑃(5,3 P(4,2) = 4. 𝐏(𝟓,𝟐)∙𝐏(𝟑,𝟐) 𝐏(𝟒,𝟐) = 120 56 150 10
  • 19. Let’s solve problem involving permutation 1. There are 4 cyclists in a race. In how many ways will they be ranked as first, second, and third placers? a. What is the value n? b. what is the value r? c. What is answer? = 4 = 3 P(4,3)= 4x3x2 = 24
  • 20. Let’s solve problem involving permutation 2. Arranging 4 different potted plants in a row. a. What is the value n? b. what is the value r? c. What is answer? = 4 = 4 P(4,4)= 4x3x2x1 = 24
  • 21. Let’s solve problem involving permutation 3. Electing a Mathematics club president, vice-president and a secretary from 10 members. a. What is the value n? b. what is the value r? c. What is answer? = 10 = 3 P(10,3)= 10x9x8 = 720
  • 22. Fundamental Counting Principle (FCP) The Fundamental Counting Principle (FCP) states that if one event has m possible outcomes and a 2nd event has n possible outcomes, then there are m⋅n total possible outcomes for the two events together.
  • 23. (GROUP ACTIVITY)- Presenter, secretary, team leader Cycling is good for health so many workers choose to use bicycle going to their workplace. Help the 5 workers reach their workplace by crossing the right way going to work.
  • 24.
  • 25. Decode: Me! Solve the problem and write the matching letter on the blank above the answer. 1) A-------- 0! 2) B-------- 4!+2! 3) K-------- P(6,2) 4) D-------- P(4,3) 5) I--------- P(7,2) 6) L-------- a horse race has 12 horses. How many different ways can first, second and third occur? 7) M-------- 8!-7! 8) N-------- The number of photographs of 10 friends taken 3 at a time. 9) O-------- In how many ways can you arrange 5 math books on a shelf? 10) S-------- P(3,3) 11) Y-------- 7!
  • 26. What are the DepED Core Values?
  • 27. What is Factorial Notation? factorial refers to the product of all positive integers less than or equal to a particular positive integer
  • 28. What is a permutation? refers to any one of all possible arrangements of the elements of the given set.
  • 29. Quiz Time! Directions: Choose the letter of the correct answer _____________1) A ________ is an arrangement of things in a definite order or ordered arrangement of objects. S. permutation M. probability I. integration L. combination _____________2) It is the product of all positive integers less that or equal to a particular positive integers. S. permutation M. Factorial Notation I. Probability E. Combination. _____________3). Evaluate 4! - 3! S. 16 M. 17 I. 18 L. 19 _____________4). Which of the following is equal to 6∙5∙4∙3∙2∙1 4∙3∙2∙1 ? S. 6! 3! M. 6! 5! E. 4! 6! L. 6! 4! _____________5. Ms. Cruz loves collecting plants. Suppose that she has 6 different potted plants and she wishes to arrange 4 of them in a row, in how many ways can this be done? E. 360 L. 720 I. 24 S. 1020
  • 30. Agreement/ Assignment Study the Combination SLM (mod 3) Reference: LM pages 285-290.