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6 Permutations& Combinations
F5
TEO POH
GURU CEMERLANG MATEMATIK
SMK ALOR AKAR, KUANTAN,
PAHANG
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6 Permutations & Combinations
PAST YEAR QUESTIONS ......
(2003) Permutations : Form Code of 3 letters
+2 digits
(2004) Permutations : arrange HEBAT
(2005) Combinations : Form debating teams of5 students
(2006) Permutations : Form 4-letter code from
UNIFORM
(2007) Combinations : Form Badminton team of 5
players : 2 boys and 3 girls
F5
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Question students always ask .....
When do we use nPr ??
... and WHEN do we use nCr ???
F5 6 Permutations & Combinations
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Ask yourself .....
Does the problem involve arrangement ?
If the order is important, then use nPr.
F5 Permutations
eg. 1. Arrange numbers 1, 2, 3, 4 to form 4-digit words
2. Arrange letters D, N, A to form 3-letter code words
3. Arrange books on a shelf
4. Arrange students (in a row) to take photos
Key word : ARRANGE
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Ask yourself ..... IsORDERimportant ???
Since order is NOT important, use nCr.
F5 Combinations
eg. 1. Choose 3 students from a class
2. Choose 5 members to form a PTA committee
3. Choose a debating team of 4 students from [2005]
4. Choose players to form badminton teams [2007]
Key word : CHOOSE
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(a) Find the number of possible arrangements, in arow, of all the cards.
(b) Find the number of these arrangements in
wh
ich
th
e letters E and A are side by side.
(a) No. of ways = 5 != 120
(b) No. of ways = 4 ! 2 != 48
F5 PERMUTATIONS AND COMBINATIONS
EA orAE
H E B A T
SPM 04
P1,Q23Q1
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Find the number offour digitnumbers which
can be formed from the numbers 1, 3, 8, 9 ifeach number is allowed to be used once only.
How many of this numbers are even ?
(a) No. of 4-digit numbers = 4 != 24
(b) No. of 4-digit even numbers
= 3 . 2 . 1 . 1= 6
F5 PERMUTATIONS AND COMBINATIONS
8 only !
Q2
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Find the number offour digit numbers exceeding3000 which can be formed from the numbers
2, 3, 6, 8, 9 if each number is allowed to be usedonce only.
No. of ways = 4 . 4. 3. 2
= 96
3, 6, 8, 9
F5 PERMUTATIONS AND COMBINATIONSQ3(a)
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Find the number ofthree-digit numbers exceeding
600 which can be formed from the numbers
3, 0, 6, 8 if each number is allowed to be usedmore thanonce.
No. of 3-Dnumbers = 2 . 4. 4= 326, 8
F5 PERMUTATIONS AND COMBINATIONS Q3(b)
(> 600) : = 32 1= 31
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Vowels : E, A, IConsonants : B, S, T, RArrangements : C V C V C V C
No. of ways = 4! 3 !
= 144
Find the number of ways the word BESTARI can bearranged so that the vowels and consonants alternate
with each other. [ 3 marks ]
F5Q4
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Given : 4 M, 2AM, 6 P (12 students)To form 5-member debating team.
(a) No. of ways = 12C5= 792(b) No. of ways = 4C1 .
6C3 .2C1
= 160
A debating team consists of 5 students. These 5 studentsare chosen from 4 monitors, 2 assistant monitors and 6
prefects.Calculate the number of ways the teams can be formed if
(a) there is no restriction,
(b) the team contains only 1 monitor and exactly 3prefects.
[ 4 marks ]
F5 SPM 05, P1,Q22
Q5
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Answers :
Given : 3 M, 2AM, 5 P (10 students)TASK : To form 4-member debating team
A debating team consists of 4 students. These
4students are chosen from
3monitors,
2assistant monitors and 5 prefects.
Calculate the number of ways the teams canbe formed if there are
(a) at least three prefects ,
(b) not more than 2 monitors. [ 4 marks ]
TryThis .!!!
Q6
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Answers :
Given : 3 M, 2AM, 5 P (10 students)TASK : To form 4-member debating team
(a) at least three prefects :
(i) 3 prefects : 5C3.5C1 = 50
(ii) 4 prefects : 5C4. 5C0 = 5
Total : 55 ways
Q6
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Answers :
Given : 3 M, 2AM, 5P (10 students)TASK : To form 4-member debating team
(b) Not more than two monitors :
(i) 0 monitor : 3C0.7C4 = 35
(ii) 1 monitor : 3C1. 7C3 = 105(iii) 2monitors : 3C2.
7C2 = 63
Total : 203 ways
Q6
