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Faktorial adalah hasil kali bilangan asli berurutan dari 1 sampai dengan n
n faktorial dinotasikan dengan n!
Jadi untuk n bilangan bulat postif, maka
n! = n x (n-1) x (n-2) x … x 3 x 2 x 1
Dalam hal ini di definisikan bahwa : 0! = 1 dan 1! = 1
CONTOH
5! = 5 x 4 x 3 x 2 x 1
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
(n+1)! = (n+1) x n x (n-1) x … x 3 x 2 x 1
DEFINISI FAKTORIAL
1.
8!
6!
HITUNGLAH
MON
TUE
WED
TUE
FRI
WKND
2.
10!
6! 5!
HITUNGLAH
MON
TUE
WED
TUE
FRI
WKND
3. Sederhanakanlah
(𝑛+1)!
𝑛−1 !
4. Tentukan nilai n yang memenuhi
persamaan
𝑛!
(𝑛−2)!
=20
5. Tentukan nilai n yang memenuhi persamaan
(𝑛+1)!
(𝑛−2)!
=
𝑛!
𝑛−4 !
CREDITS: This presentation template was created by
Slidesgo, including icons by Flaticon, infographics &
images by Freepik
TERIMA
KASIH
SELAMAT BELAJAR
TUE
WED
FRI
WKND
THU
PERMUTASI
Permutasi adalah cara
penyusunan suatu percobaan
atau kejadian yang
memperhatikan urutan
Kombinasi adalah cara
penyusunan suatu percobaan
atau kejadian TANPA
memperhatikan urutan
KOMBINASI
Contoh
Misalkan kita memilih dua orang yang
akan menjadi juara 1 dan juara 2, dan
yang terpilih A dan B. Jika A juara 1
dan B juara 2 tentunya akan
berbeda jika B juara 1 dan A juara 2,
atau secara urutan AB ≠ BA
Contoh
Misalkan kita memilih dua orang yang
akan mewakili sebuah tim, kemudian
terpilihlah A dan B. Dalam hal ini,
tentunya terpilih A dan B akan sama
dengan terpilihnya B dan A. sehingga
secara urutan AB = BA
WED
FRI
WKND
THU
Permutasi yang memuat
beberapa unsur yang sama
Permutasi dengan susunan
yang berbeda
Permutasi yang memuat
beberapa unsur yang sama
Permutasi siklis
PERMUTASI
Permutasi r unsur dari n
unsur yang tersedia,
Tentukan nilai permutasi berikut :
a. 5P2
a. 7P3
CONTOH SOAL
Seorang satpam bank ingin mencetak nomor antrian nasabah yang terdiri dari tiga
angka. Jika nomor antrian tersebut tidak memuat angka yang sama yang dibentuk
dari angka 1, 2, 3, 4. Banyak pilihan nomor antrian yang dapat dibuat adalah…
Dalam suatu kepengurusan yang beranggotakan 10 orang akan dipilih pengurus yang
terdiri atas ketua, wakil ketua, sekretaris, dan bendahara. Banyak susunan pengurus
berbeda yangdapat dibentuk adalah
…
CONTOH SOAL
A TIMELINE ALWAYS WORKS
WELL
VENUS
Venus has a
beautiful name
SATURN
It’s a gas giant and
the ringed planet
MARS
Despite being red,
Mars is a cold
JUPITER
It’s a gas giant and
the largest planet
WKND
“This is a quote, words full of wisdom
that someone important said and can
make the reader get inspired.”
—SOMEONE
FAMOUS
MON
TUE
WED
THU
FRI
WKND
MON
TUE
WED
TUE
FRI
WKND
Permuatasi yang memuat beberapa unsur yang
sama
Tentukan nilai permutasi berikut :
a. 5P2
a. 7P3
CONTOH SOAL
01
02
03
MONDAY
Here you could describe
the topic of the section
TUESDAY
Here you could describe
the topic of the section
WEDNESDAY
Here you could describe
the topic of the section
TABLE OF CONTENTS
THURSDAY
Here you could describe
the topic of the section
FRIDAY
Here you could describe
the topic of the section
WEEKEND
Here you could describe
the topic of the section
04
05
06
MON
TUE
WED
TUE
FRI
WKND
THE WEEK BEGINS
You could enter a subtitle here
if you need it
01
MON
TUE
WED
TUE
FRI
WKND
Do you know what helps you make
your point clear?
Lists like this one:
● They’re simple
● You can organize your ideas
clearly
● You’ll never forget to buy milk!
And the most important thing: the
audience won’t miss the point of
your presentation
THE SLIDE TITLE GOES HERE!
MON
TUE
WED
TUE
FRI
WKND
A PICTURE ALWAYS
REINFORCES THE CONCEPT
Images reveal large amounts
of data, so remember: use an
image instead of a long text
MON
TUE
WED
TUE
FRI
WKND
Mercury is the closest planet
to the Sun and the smallest
one in the Solar System
MERCURY
Venus has a beautiful name
and is the second planet from
the Sun. It’s terribly hot
VENUS
MAYBE YOU NEED TO DIVIDE
THE CONTENT
WED
FRI
WKND
THU
A PICTURE IS WORTH
A THOUSAND WORDS
AWESOME
WORDS
FRI
WKND
THU
USE A GRAPH TO SHOW
YOUR DATA
To modify this graph, click on it, follow the link,
change the data and paste the resulting graph here
5,000 3,800
5,400
MARS
Mars is actually a
cold place
VENUS
Venus has a
beautiful name
FRI
WKND
THU
YOU CAN ALSO ORGANIZE
DATA IN A TABLE
MASS
(earths)
DIAMETER
(earths)
MERCURY 0.06 0.38
MARS 0.11 0.53
SATURN 95.2 9.4
FRI
WKND
THU
THURSDAY
DAY 1
Mars is actually a
cold place
DAY 2
Venus has a
beautiful name
DAY 3
It’s a gas giant and
the largest
DAY 4
It’s the closest
planet to the Sun
FRI
WKND
THU
INFOGRAPHICS
MERCURY
Mercury is a
small planet
Venus has a
beautiful name
VENUS
JUPITER
Jupiter is the
biggest planet
MARS
It’s actually a
cold place
10% 20%
30% 40%
FRI
WKND
Despite being red, Mars is
actually a cold place full of
iron oxide dust
JOHN DOE
Saturn is a gas giant,
composed mostly of
hydrogen and helium
SARAH DOE
OUR TEAM
FRI
WKND
SATURN
It’s composed
mostly of hydrogen
and helium
VENUS
It has a beautiful
name and is the
second planet
MERCU
RY
It’s the closest
planet to the Sun
and the smallest
OUR SUCCESS
FRI
WKND
MERCURY
It’s the smallest planet in
the Solar System
MARS
Despite being red, it’s
actually a cold place
VENUS
It has a beautiful name
and is the second planet
SATURN
It’s composed mostly of
hydrogen and helium
FRIDAY
FRI
WKND
THIS IS A MAP
MARS
Mars is a cold place. It’s
full of iron oxide dust
VENUS
It has a beautiful name
and is the second planet
SATURN
It’s composed of
hydrogen and helium
WKND
THESE ARE PERCENTAGES
30%
MARS
Despite being red,
Mars is a cold place
70%
MERCURY
It’s the smallest planet
in the Solar System
WKND
MERCURY
Mercury is the closest planet to
the Sun and the smallest
VENUS
It has a beautiful name and is the
second planet from the Sun
WEEKEND
WKND
TARGET
GENDER
AGE
AVERAGE EXPENSES
40% 500.00
60%
EDUCATION LEVEL
20-40
41-60
High School
Average spend per customer
University
40%
60%
70%
30%
4,498,30 Big numbers catch your
audience’s attention
earths is the Sun’s mass
is Jupiter’s rotation period
between Earth and the Moon
333,000.00
24h 37m 23s
386,000 km
SPECIAL REMINDERS
You could write here
your own notes
SATURN
It’s composed mostly of
hydrogen and helium
VENUS
It has a beautiful name
and is the second planet
OUR SERVICES
Despite being red,
Mars is cold
It’s the closest
planet to the Sun
Venus has a
beautiful name
MARS
VENUS
MERCURY NEPTUNE
$35
$60
$85
$20
Neptune is the
farthest planet
OUR PARTNERS
Here you could
talk a bit about
this person
CLEVER CHARLENE
Here you could
talk a bit about
this person
HELEN JAMES
Here you could
talk a bit about
this person
LAURA MCKANE
Here you could
talk a bit about
this person
JENNA DOE
LET’S USE ANOTHER
INFOGRAPHIC!
MARS
Mars is a very
cold place
JUPITER
Jupiter is the
biggest planet
SATURN
It’s a gas giant
and has rings
VENUS
Venus has a
beautiful name
10%
30%
10%
30%
DESKTOP SOFTWARE
You can replace the image on
the screen with your own work.
Just delete this one, add yours
and center it properly
TABLET APP
You can replace the
image on the screen with
your own work. Just
delete this one, add yours
and center it properly
MOBILE WEB
You can replace the image on
the screen with your own work.
Just delete this one, add yours
and center it properly
ALTERNATIVE RESOURCES
RESOURCES
Did you like the resources on this template? Get them for free at our other websites.
Vectors
● Bullet journal planner template
● Bullet journal planner template
● Realistic bullet journal with drawings and doodles
● Realistic bullet journal with doodle drawings
● Bullet journal planner template
● Realistic bullet journal with drawings and doodles
● School timetable template with pens and pencils
Photos
● High angle view of a person's hand writing on card with light bulb
● Portrait of adult woman holding dog while working
● Realistic bullet journal with drawings and doodles
● Desk with notebook message boss day
Instructions for use
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Fonts & colors used
This presentation has been made using the following fonts:
Sue Ellen Francisco
(https://fonts.google.com/specimen/Sue+Ellen+Francisco)
Roboto Slab
(https://fonts.google.com/specimen/Roboto+Slab)
#ffe790 #ffab40 #df8602
#ffd200
Stories by Freepik
Create your Story with our illustrated concepts. Choose the style you like the most, edit its colors, pick
the background and layers you want to show and bring them to life with the animator panel! It will boost
your presentation. Check out How it Works.
Pana Amico Bro Rafiki Cuate
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JANUARY FEBRUARY MARCH APRIL
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faktorial.pptx

  • 1.
  • 2. Faktorial adalah hasil kali bilangan asli berurutan dari 1 sampai dengan n n faktorial dinotasikan dengan n! Jadi untuk n bilangan bulat postif, maka n! = n x (n-1) x (n-2) x … x 3 x 2 x 1 Dalam hal ini di definisikan bahwa : 0! = 1 dan 1! = 1 CONTOH 5! = 5 x 4 x 3 x 2 x 1 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 (n+1)! = (n+1) x n x (n-1) x … x 3 x 2 x 1 DEFINISI FAKTORIAL
  • 4. HITUNGLAH MON TUE WED TUE FRI WKND 3. Sederhanakanlah (𝑛+1)! 𝑛−1 ! 4. Tentukan nilai n yang memenuhi persamaan 𝑛! (𝑛−2)! =20
  • 5. 5. Tentukan nilai n yang memenuhi persamaan (𝑛+1)! (𝑛−2)! = 𝑛! 𝑛−4 !
  • 6. CREDITS: This presentation template was created by Slidesgo, including icons by Flaticon, infographics & images by Freepik TERIMA KASIH SELAMAT BELAJAR
  • 7.
  • 8. TUE WED FRI WKND THU PERMUTASI Permutasi adalah cara penyusunan suatu percobaan atau kejadian yang memperhatikan urutan Kombinasi adalah cara penyusunan suatu percobaan atau kejadian TANPA memperhatikan urutan KOMBINASI Contoh Misalkan kita memilih dua orang yang akan menjadi juara 1 dan juara 2, dan yang terpilih A dan B. Jika A juara 1 dan B juara 2 tentunya akan berbeda jika B juara 1 dan A juara 2, atau secara urutan AB ≠ BA Contoh Misalkan kita memilih dua orang yang akan mewakili sebuah tim, kemudian terpilihlah A dan B. Dalam hal ini, tentunya terpilih A dan B akan sama dengan terpilihnya B dan A. sehingga secara urutan AB = BA
  • 9. WED FRI WKND THU Permutasi yang memuat beberapa unsur yang sama Permutasi dengan susunan yang berbeda Permutasi yang memuat beberapa unsur yang sama Permutasi siklis PERMUTASI Permutasi r unsur dari n unsur yang tersedia,
  • 10. Tentukan nilai permutasi berikut : a. 5P2 a. 7P3 CONTOH SOAL
  • 11. Seorang satpam bank ingin mencetak nomor antrian nasabah yang terdiri dari tiga angka. Jika nomor antrian tersebut tidak memuat angka yang sama yang dibentuk dari angka 1, 2, 3, 4. Banyak pilihan nomor antrian yang dapat dibuat adalah… Dalam suatu kepengurusan yang beranggotakan 10 orang akan dipilih pengurus yang terdiri atas ketua, wakil ketua, sekretaris, dan bendahara. Banyak susunan pengurus berbeda yangdapat dibentuk adalah … CONTOH SOAL
  • 12. A TIMELINE ALWAYS WORKS WELL VENUS Venus has a beautiful name SATURN It’s a gas giant and the ringed planet MARS Despite being red, Mars is a cold JUPITER It’s a gas giant and the largest planet WKND
  • 13. “This is a quote, words full of wisdom that someone important said and can make the reader get inspired.” —SOMEONE FAMOUS MON TUE WED THU FRI WKND MON TUE WED TUE FRI WKND Permuatasi yang memuat beberapa unsur yang sama
  • 14. Tentukan nilai permutasi berikut : a. 5P2 a. 7P3 CONTOH SOAL
  • 15. 01 02 03 MONDAY Here you could describe the topic of the section TUESDAY Here you could describe the topic of the section WEDNESDAY Here you could describe the topic of the section TABLE OF CONTENTS THURSDAY Here you could describe the topic of the section FRIDAY Here you could describe the topic of the section WEEKEND Here you could describe the topic of the section 04 05 06 MON TUE WED TUE FRI WKND
  • 16. THE WEEK BEGINS You could enter a subtitle here if you need it 01 MON TUE WED TUE FRI WKND
  • 17. Do you know what helps you make your point clear? Lists like this one: ● They’re simple ● You can organize your ideas clearly ● You’ll never forget to buy milk! And the most important thing: the audience won’t miss the point of your presentation THE SLIDE TITLE GOES HERE! MON TUE WED TUE FRI WKND
  • 18. A PICTURE ALWAYS REINFORCES THE CONCEPT Images reveal large amounts of data, so remember: use an image instead of a long text MON TUE WED TUE FRI WKND
  • 19. Mercury is the closest planet to the Sun and the smallest one in the Solar System MERCURY Venus has a beautiful name and is the second planet from the Sun. It’s terribly hot VENUS MAYBE YOU NEED TO DIVIDE THE CONTENT WED FRI WKND THU
  • 20. A PICTURE IS WORTH A THOUSAND WORDS
  • 22. USE A GRAPH TO SHOW YOUR DATA To modify this graph, click on it, follow the link, change the data and paste the resulting graph here 5,000 3,800 5,400 MARS Mars is actually a cold place VENUS Venus has a beautiful name FRI WKND THU
  • 23. YOU CAN ALSO ORGANIZE DATA IN A TABLE MASS (earths) DIAMETER (earths) MERCURY 0.06 0.38 MARS 0.11 0.53 SATURN 95.2 9.4 FRI WKND THU
  • 24. THURSDAY DAY 1 Mars is actually a cold place DAY 2 Venus has a beautiful name DAY 3 It’s a gas giant and the largest DAY 4 It’s the closest planet to the Sun FRI WKND THU
  • 25. INFOGRAPHICS MERCURY Mercury is a small planet Venus has a beautiful name VENUS JUPITER Jupiter is the biggest planet MARS It’s actually a cold place 10% 20% 30% 40% FRI WKND
  • 26. Despite being red, Mars is actually a cold place full of iron oxide dust JOHN DOE Saturn is a gas giant, composed mostly of hydrogen and helium SARAH DOE OUR TEAM FRI WKND
  • 27. SATURN It’s composed mostly of hydrogen and helium VENUS It has a beautiful name and is the second planet MERCU RY It’s the closest planet to the Sun and the smallest OUR SUCCESS FRI WKND
  • 28. MERCURY It’s the smallest planet in the Solar System MARS Despite being red, it’s actually a cold place VENUS It has a beautiful name and is the second planet SATURN It’s composed mostly of hydrogen and helium FRIDAY FRI WKND
  • 29. THIS IS A MAP MARS Mars is a cold place. It’s full of iron oxide dust VENUS It has a beautiful name and is the second planet SATURN It’s composed of hydrogen and helium WKND
  • 30. THESE ARE PERCENTAGES 30% MARS Despite being red, Mars is a cold place 70% MERCURY It’s the smallest planet in the Solar System WKND
  • 31. MERCURY Mercury is the closest planet to the Sun and the smallest VENUS It has a beautiful name and is the second planet from the Sun WEEKEND WKND
  • 32. TARGET GENDER AGE AVERAGE EXPENSES 40% 500.00 60% EDUCATION LEVEL 20-40 41-60 High School Average spend per customer University 40% 60% 70% 30%
  • 33. 4,498,30 Big numbers catch your audience’s attention
  • 34. earths is the Sun’s mass is Jupiter’s rotation period between Earth and the Moon 333,000.00 24h 37m 23s 386,000 km
  • 35. SPECIAL REMINDERS You could write here your own notes SATURN It’s composed mostly of hydrogen and helium VENUS It has a beautiful name and is the second planet
  • 36. OUR SERVICES Despite being red, Mars is cold It’s the closest planet to the Sun Venus has a beautiful name MARS VENUS MERCURY NEPTUNE $35 $60 $85 $20 Neptune is the farthest planet
  • 37. OUR PARTNERS Here you could talk a bit about this person CLEVER CHARLENE Here you could talk a bit about this person HELEN JAMES Here you could talk a bit about this person LAURA MCKANE Here you could talk a bit about this person JENNA DOE
  • 38. LET’S USE ANOTHER INFOGRAPHIC! MARS Mars is a very cold place JUPITER Jupiter is the biggest planet SATURN It’s a gas giant and has rings VENUS Venus has a beautiful name 10% 30% 10% 30%
  • 39. DESKTOP SOFTWARE You can replace the image on the screen with your own work. Just delete this one, add yours and center it properly
  • 40. TABLET APP You can replace the image on the screen with your own work. Just delete this one, add yours and center it properly
  • 41. MOBILE WEB You can replace the image on the screen with your own work. Just delete this one, add yours and center it properly
  • 43. RESOURCES Did you like the resources on this template? Get them for free at our other websites. Vectors ● Bullet journal planner template ● Bullet journal planner template ● Realistic bullet journal with drawings and doodles ● Realistic bullet journal with doodle drawings ● Bullet journal planner template ● Realistic bullet journal with drawings and doodles ● School timetable template with pens and pencils Photos ● High angle view of a person's hand writing on card with light bulb ● Portrait of adult woman holding dog while working ● Realistic bullet journal with drawings and doodles ● Desk with notebook message boss day
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  • 45. Fonts & colors used This presentation has been made using the following fonts: Sue Ellen Francisco (https://fonts.google.com/specimen/Sue+Ellen+Francisco) Roboto Slab (https://fonts.google.com/specimen/Roboto+Slab) #ffe790 #ffab40 #df8602 #ffd200
  • 46. Stories by Freepik Create your Story with our illustrated concepts. Choose the style you like the most, edit its colors, pick the background and layers you want to show and bring them to life with the animator panel! It will boost your presentation. Check out How it Works. Pana Amico Bro Rafiki Cuate
  • 47. You can easily resize these resources without losing quality. To change the color, just ungroup the resource and click on the object you want to change. Then, click on the paint bucket and select the color you want. Group the resource again when you’re done. You can also look for more infographics on Slidesgo. Use our editable graphic resources...
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  • 49.
  • 50. JANUARY FEBRUARY MARCH APRIL PHASE 1 Task 1 Task 2 JANUARY FEBRUARY MARCH APRIL MAY JUNE PHASE 1 PHASE 2 Task 1 Task 2 Task 1 Task 2
  • 51.
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  • 53. ...and our sets of editable icons You can resize these icons without losing quality. You can change the stroke and fill color; just select the icon and click on the paint bucket/pen. In Google Slides, you can also use Flaticon’s extension, allowing you to customize and add even more icons.
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