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PERMUTATIONS
PERMUTATIONSMENYUSUN, SUSUNAN
SUSUNAN BENDA / BARANG
SUSUNAN KEDUDUKAN ORANG
SUSUNAN NOMBOR / KOD
05/03/23
2
PERMUTATION
3 KAD WARNA DISUSUN SEBARIS, ADA BERAPA KEMUNGKINAN SUSUNAN
05/03/23
3
PERMUTATION
3 KAD WARNA DISUSUN SEBARIS, ADA BERAPA KEMUNGKINAN SUSUNAN
05/03/23
4
PERMUTATION
3 KAD WARNA DISUSUN SEBARIS, ADA BERAPA KEMUNGKINAN SUSUNAN
05/03/23
5
PERMUTATION
3 KAD WARNA DISUSUN SEBARIS, ADA BERAPA KEMUNGKINAN SUSUNAN
05/03/23
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PERMUTATION
3 KAD WARNA DISUSUN SEBARIS, ADA BERAPA KEMUNGKINAN SUSUNAN
05/03/23
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PERMUTATION
3 KAD WARNA DISUSUN SEBARIS, ADA BERAPA KEMUNGKINAN SUSUNAN
05/03/23
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PERMUTATION
3 KAD NOMBOR DISUSUN SEBARIS, ADA BERAPA KEMUNGKINAN SUSUNAN NOMBOR TIGA DIGIT
05/03/23
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PERMUTATION
05/03/23
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PERMUTATION
05/03/23
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PERMUTATION
05/03/23
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PERMUTATION
05/03/23
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PERMUTATION
05/03/23
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PERMUTATION
05/03/23
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PERMUTATION
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321ADA 6 NOMBOR TIGA DIGIT
05/03/23
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LEARNING OBJECTIVES Students will be taught to:1. Understand and use the concept
of permutation.
LEARNING OUTCOMES
Students will be able to: Determine the total number of ways to perform successive events
using multiplication rule.
Example : From SESMA to HSNZ There are 2 routes joining SESMA and BUKIT BESAR and 3
routes joining BUKIT BESAR and HSNZ.Find the number of different ways of traveling from SESMA
to HSNZ via BUKIT BESAR.
BUKIT BESAR
JAMBATAN
MANIRSESMA HSNZ
GONG KAPAS/BATU BURUK
JPJ/POLIS
GONG KAPAS / SMAK
SESMA
(1) JAMBATAN SULTAN MAHMUD
BUKIT BESAR
(3) GONG KAPAS / BATU BUROK
HSNZ(4) JPJ / POLIS
(2) MANIR (4) GONG KAPAS / SMA KHAIRIAH
Kemungkinan : Laluan 1 : (1) , (3) Laluan 2 : (1) , (4) Laluan 3 : (1) , (5)Laluan 4 : (2) , (3) Laluan 5 : (2) , (4) Laluan 6 : (2) , (5) Oleh itu : Terdapat 6 cara yang berbeza dari SESMA ke HSNZ Multiplication Rule : From SESMA to BUKIT BESAR = 2 cara
From BUKIT BESAR to HSNZ = 3 cara Bilangan cara = 2 x 3 = 6
There are 3 routes joining village A and village B and 4 routes joining village B and village C. Find the number of different ways of traveling from village A to village C via village B.
3 4 12cara
There are 2 bus companies that provide transport from town E to town F and 3 bus companies that provide transport from town F to town G. Find the number of ways a person can travel from town E via to town G via town F by taking a bus. 2 3 6cara
A B C D 1 2 3
The diagram above shows cards of a game. If a player is going to select a letter card and a digit card, find the number of different ways can this be done.
4 3 12cara
LEARNING OUTCOMESStudents will be able to:
Determine the number of permutations of n different objects.
or
nnn
nPn
n
1!
!)(!
! ( 1)( 2)........(3)(2)(1)n n n n
The diagram below shows eight cards with different letters on it. Find the number of arrangements if all the cards are used without restriction.
C O M P U T E R
8 7 6 5 4 3 2 1
Number of arrangements = 8x7x6x 5x4x3x2x1 = 40 320
Or use ; = 40 32088P
In how many different ways can 5 different books be arranged on a shelf ?
In how many different ways can 4 different presents can be given to 4 children ?
5! 120 cara
4! 24 cara
In how many ways can the letters of the word ‘GRADIENT’ be arranged ?
How many five-digit numbers can be formed using the digits 2,3,7, 8 and 9 without repetition ?
8! 40320 cara
5! 120 cara
LEARNING OUTCOMESStudents will be able to:
Determine the number of permutations of n different objects taken r at a time for given conditions.
!
( )!nr
nPn r
How many four-digit numbers can you form using the digits 2, 3, 5, 6 and 7 ?
45 120P cara
1 2 4 6
4 keping kad bernombor disusun
3 keping kad bernombor disusun
Berapa nombor ganjil 3 digit yang boleh dibentuk ?
4! 24 cara
34 24P cara
1 21 3 6P P cara
1 2 4 6
Berapa nombor genap 4 digit yang boleh dibentuk ? Berapa nombor genap 3 digit yang boleh dibentuk ?
Berapa nombor ganjil 4 digit > 3000 yang boleh dibentuk ?
33 3 18P cara
Diagram below shows eight letter cards. A five-letter code is to be formed using five of these cards. Find the number of different five-letter codes that can be formed which start with a vocal.
B O C D U F A V
7 6 5 4
Number of arrangement = 3x7x6x 5x4 = 2520 or use = = 25204
71
3 PP
3
Diagram below shows eight letter cards. A five-letter code is to be formed using five of these cards. Find the number of different five-letter codes that can be formed which start with letter “X” and end with letter “O”.
A P E X S O F T
6 5 4 1
Number of arrangement = 1x6x5x4x1 = 120 or use, = 1203
6P
1
Diagram below shows seven cards with different digits. Find the number of 4-digit numbers that can be form if the number formed is an even number.
1 2 3 4 5 6 7
6 5 4 3
Numbers can be form = 6x5x4x3 = 360 or use , = 3601
33
6 PP
A 4 - digit number is to be formed from digits 0, 1, 2, 3, 4, 5 and 6 without using any digit more than once. Find the number of possible four-digits numbers that can be formed if the number formed is greater than 2 500.
0 1 2 3 4 5 6
4
Number can be formed = 1x2x5x4 = 40 or use ; = 402
51
21
1 PPP
1 2 5
Case 1
A 4 - digit number is to be formed from digits 0, 1, 2, 3, 4, 5 and 6 without using any digit more than once. Find the number of possible four-digits numbers that can be formed if the number formed is greater than 2 500.
0 1 2 3 4 5 6
4
Number can be formed= 4x6x5x4 = 480 Or use ; = 4803
61
4 PP
4 6 5
Case 2
A 4 - digit number is to be formed from digits 0, 1, 2, 3, 4, 5 and 6 without using any digit more than once. Find the number of possible four-digits numbers that can be formed if the number formed is greater than 2 500.
Numbers can be formed greater than 2 500.
= (4x6x5x4) + (1x2x5x4 )= 480 + 40 = 520
)()( 25
12
11
36
14 PPPPP =520
or
L1L2L2L1
Diagram belows shows 2 boys and 5 girls in a rows. Find the number of these arrangements in which the two boys are side by side.
L1 L2 G3 G4 G5 G6 G7
Number of arrangement for 2 boys = 22
2PL1L2
Number of arrangement for 6 boys = =720 6
6P Sum of arrangement = 2x720 = 1440
How many ordered arrangements are there if we want to arrange 5 out of 12 basket players ?
[95040]In how many different ways can 3 of the letters in the word ‘ PROGRAM ‘ be arranged without repetition ?
[210]
how many different ways can 2 of the letters in the word ‘ ‘be arranged without repetition ?
20]How many four-digit numbers can you form using the digits 2, 3, 5, 6 and 7 ?
120]