Psalms 14: 1-3
The fool hath said in his heart, there is no God.
They are corrupt, they have done abominable
works, there is none that doeth good. The
LORD looked down from heaven upon the
children of men, to see if there were any that
did understand, and seek God. They are all
gone aside, they are all together become filthy;
there is none that doeth good, no not one.
Let Us Pray
O Lord God who created heaven and earth , we
praise and thank you for the gift of life and for your
guidance and protection. We beseech you to
enlighten our young minds to grasp the lessons we
are about to learn. Bless each one of us with wisdom
and understanding to retain all information and
concepts taught by our teachers. Guide and bless
our teachers for them to teach us in a creative way.
These we ask through Jesus Christ, our Lord and
savior , amen.
Objectives:
• Illustrate permutation of object.
• Derive the Formula for finding the
number of permutation of n objects
taken r at a time.
• Solves problems involving permutation.
PRETEST
Directions: Apply formula in finding
Permutation of n objects taken r at a time.
Write only the letter of the correct answer.
1. What is P(8,5)?
A. 56
B. 336
C. 1,400
D. 6,720
PRETEST
Directions: Apply formula in finding
Permutation of n objects taken r at a time.
Write only the letter of the correct answer.
2. If P( 9,r ) = 3,024, what is r ?
A. 2
B. 4
C. 5
D. 6
PRETEST
Directions: Apply formula in finding
Permutation of n objects taken r at a time.
Write only the letter of the correct answer.
3. If P( n,4 ) = 5,040, which of the following
is the value of n?
A. 12
B. 10
C. 9
D. 8
PRETEST
Directions: Apply formula in finding
Permutation of n objects taken r at a time.
Write only the letter of the correct answer.
4. What is the total number of different
permutations of all the letters of
the word MATH?
A. 48
B. 36
C. 24
D. 12
PRETEST
Directions: Apply formula in finding
Permutation of n objects taken r at a time.
Write only the letter of the correct answer.
5. In how many ways can 9 different
books be arranged on a shelf?
A. 5,040
B. 9,000
C. 120,000
D. 362,880
RECAP
Evaluate:
1.
2.
7!
4!
8!
2! 4!
=210 3.
= 840 4.
10!
5!2!
= 15,120
9!
(8−3)!
=3,024
RECAP
Evaluate:
1.
7!
4!
7 𝑥 6 𝑥 5 𝑥 4!
=
4!
=7x6x5 =210
Divide common
factors between
numerator and
denominator
RECAP
Evaluate:
2.
8!
=
2! 4!
3
8 𝑥 7𝑥 6 𝑥 5 𝑥 4! 8 𝑥 7𝑥 6 𝑥 5
=
2𝑥1
2 𝑥 1 𝑥 4!
=8 x 7 x 3 x 5 = 840
RECAP
Evaluate:
10!
10 𝑥 9 𝑥 8 𝑥 7 𝑥 6 𝑥 5!
=
3.
5! 𝑥 2 𝑥 1
5!2!
3
10 𝑥 9 𝑥 8 𝑥 7𝑥 6
=
= 10 x 9 x 8 x 7 x 3
2
= 15,120
RECAP
Evaluate:
4.
9!
(8−3)!
=
9 𝑥 8 𝑥 7𝑥 6 𝑥 5!
5!
=9x8x7x6
=3,024
Two days before typhoon Odette, you decided to
buy plastic boxes for safekeeping of important
items. Your money is just enough to buy 3 boxes.
You have 8 items to place inside each box.
There are 8 items to keep, but you only have 3 boxes
where only 1 item can be placed in each box. How
many options do you have if your are going to
choose only3 items according to each importance?
Watch laptop mobile phone shoes
Book tablet
bracelet
shirt
What will you place inside the first ,
second, and third box?
Watch
Book
laptop
tablet
mobile phone shoes
bracelet
shirt
Remember that…
Watch
Book
laptop
tablet
mobile phone
bracelet
shoes
shirt
By the Fundamental Counting Principle (FCP)
8x7x6
8x7x6
𝟖 𝒙 𝟕 𝒙 𝟔 𝒙 𝟓!
8x7x6=
𝟓!
𝟖!
=
𝟓!
8x7x6
𝟖!
=
𝟓!
There are 8 items to
be placed inside the
box
There are 5
remaining items that
were not chosen
𝟖!
=
𝟓!
𝟖!
=
(𝟖 − 𝟑)!
If we let 8 = n and 3 = r
The Permutation Formula
The permutation of n objects taken r
at a time is denoted by
The Permutation Formula
Comes in other
notation:
Solving the given scenario by the Permutation
Formula:
Solution:
n=8 r=3
Solution:
Solution:
Solution:
Examples:
Solution:
Solution:
Wrap Up
POST TEST
Answers Key:
Activity 1
1.) 12 2.) 30 3.) 720
4.) 836
Activity 2
1.) 120
2.) 4 3.) 9
4.) 3
Activity 3
1.) 24 2.) 1,685,040
5.) 90
5.) 3,600
5.) 15
3.) 2,520
Post Test
1.) B
2.) B 3.) C
4.) D
4.) 1,680
5.) D
If your score is
15 up
= Keep It Up !
14 below =
Keep
practicing !