1. The Basic Counting Principle

2. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.

3. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.
e.g. 3 dice are rolled

4. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.
e.g. 3 dice are rolled
(i) How many ways can the three dice fall?

5. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.
e.g. 3 dice are rolled
(i) How many ways can the three dice fall?
Ways  6  6  6

6. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.
e.g. 3 dice are rolled
(i) How many ways can the three dice fall?
the 1st die has 6 possibilities
Ways  6  6  6

7. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.
e.g. 3 dice are rolled
(i) How many ways can the three dice fall?
the 1st die has 6 possibilities
the 2nd die has 6 possibilities
Ways  6  6  6

8. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.
e.g. 3 dice are rolled
(i) How many ways can the three dice fall?
the 1st die has 6 possibilities
the 2nd die has 6 possibilities
Ways  6  6  6 the 3rd die has 6 possibilities

9. The Basic Counting Principle
If one event can happen in m different ways and after this another
event can happen in n different ways, then the two events can
occur in mn different ways.
e.g. 3 dice are rolled
(i) How many ways can the three dice fall?
the 1st die has 6 possibilities
the 2nd die has 6 possibilities
Ways  6  6  6 the 3rd die has 6 possibilities
 216

10. (ii) How many ways can all three dice show the same number?

11. (ii) How many ways can all three dice show the same number?
Ways  6 11

12. (ii) How many ways can all three dice show the same number?
the 1st die has 6 possibilities
Ways  6 11

13. (ii) How many ways can all three dice show the same number?
the 1st die has 6 possibilities
the 2nd die now has only 1 possibility
Ways  6 11

14. (ii) How many ways can all three dice show the same number?
the 1st die has 6 possibilities
the 2nd die now has only 1 possibility
Ways  6 11
the 3rd die now has only 1 possibility

15. (ii) How many ways can all three dice show the same number?
the 1st die has 6 possibilities
the 2nd die now has only 1 possibility
Ways  6 11
6 the 3rd die now has only 1 possibility

16. (ii) How many ways can all three dice show the same number?
the 1st die has 6 possibilities
the 2nd die now has only 1 possibility
Ways  6 11
6 the 3rd die now has only 1 possibility
(iii) What is the probability that all three dice show the same
number?

17. (ii) How many ways can all three dice show the same number?
the 1st die has 6 possibilities
the 2nd die now has only 1 possibility
Ways  6 11
6 the 3rd die now has only 1 possibility
(iii) What is the probability that all three dice show the same
number?
6
Pall 3 the same 
216

18. (ii) How many ways can all three dice show the same number?
the 1st die has 6 possibilities
the 2nd die now has only 1 possibility
Ways  6 11
6 the 3rd die now has only 1 possibility
(iii) What is the probability that all three dice show the same
number?
6
Pall 3 the same 
216
1

36

19. 1996 Extension 1 HSC Q5c)
Mice are placed in the centre of a maze which has five exits.
Each mouse is equally likely to leave the maze through any of the
five exits. Thus, the probability of any given mouse leaving by a
particular exit is 1
5
Four mice, A, B, C and D are put into the maze and behave
independently.
(i) What is the probability that A, B, C and D all come out the same
exit?

20. 1996 Extension 1 HSC Q5c)
Mice are placed in the centre of a maze which has five exits.
Each mouse is equally likely to leave the maze through any of the
five exits. Thus, the probability of any given mouse leaving by a
particular exit is 1
5
Four mice, A, B, C and D are put into the maze and behave
independently.
(i) What is the probability that A, B, C and D all come out the same
exit?
1 1 1
Pall use the same exit   1  
5 5 5

21. 1996 Extension 1 HSC Q5c)
Mice are placed in the centre of a maze which has five exits.
Each mouse is equally likely to leave the maze through any of the
five exits. Thus, the probability of any given mouse leaving by a
particular exit is 1
5
Four mice, A, B, C and D are put into the maze and behave
independently.
(i) What is the probability that A, B, C and D all come out the same
exit?
First mouse can go through any door  P  1
1 1 1
Pall use the same exit   1  
5 5 5

22. 1996 Extension 1 HSC Q5c)
Mice are placed in the centre of a maze which has five exits.
Each mouse is equally likely to leave the maze through any of the
five exits. Thus, the probability of any given mouse leaving by a
particular exit is 1
5
Four mice, A, B, C and D are put into the maze and behave
independently.
(i) What is the probability that A, B, C and D all come out the same
exit?
First mouse can go through any door  P  1
Other mice must go
1 1 1 1
Pall use the same exit   1   through same door  P 
5 5 5 5

23. 1996 Extension 1 HSC Q5c)
Mice are placed in the centre of a maze which has five exits.
Each mouse is equally likely to leave the maze through any of the
five exits. Thus, the probability of any given mouse leaving by a
particular exit is 1
5
Four mice, A, B, C and D are put into the maze and behave
independently.
(i) What is the probability that A, B, C and D all come out the same
exit?
First mouse can go through any door  P  1
Other mice must go
1 1 1 1
Pall use the same exit   1   through same door  P 
5 5 5 5
1

125

24. (ii) What is the probability that A, B and C come out the same
exit and D comes out a different exit?

25. (ii) What is the probability that A, B and C come out the same
exit and D comes out a different exit?
4 1 1
P ABC use same exit, D uses different exit   1  
5 5 5

26. (ii) What is the probability that A, B and C come out the same
exit and D comes out a different exit?
D can go through any door  P  1
4 1 1
P ABC use same exit, D uses different exit   1  
5 5 5

27. (ii) What is the probability that A, B and C come out the same
exit and D comes out a different exit?
D can go through any door  P  1
4 1 1
P ABC use same exit, D uses different exit   1  
5 5 5
Next mouse has 4 doors to choose
4
P 
5

28. (ii) What is the probability that A, B and C come out the same
exit and D comes out a different exit?
D can go through any door  P  1
4 1 1
P ABC use same exit, D uses different exit   1  
5 5 5
Next mouse has 4 doors to choose
4
P 
5 Other mice must go
1
through same door  P 
5

29. (ii) What is the probability that A, B and C come out the same
exit and D comes out a different exit?
D can go through any door  P  1
4 1 1
P ABC use same exit, D uses different exit   1  
5 5 5
4
Next mouse has 4 doors to choose 
125
4
P 
5 Other mice must go
1
through same door  P 
5

30. (iii) What is the probability that any of the four mice come out the
same exit and the other comes out a different exit?

31. (iii) What is the probability that any of the four mice come out the
same exit and the other comes out a different exit?
4
P D uses different exit  
125

32. (iii) What is the probability that any of the four mice come out the
same exit and the other comes out a different exit?
4
P D uses different exit  
4 125
 P A uses different exit  
125

33. (iii) What is the probability that any of the four mice come out the
same exit and the other comes out a different exit?
4
P D uses different exit  
4 125
 P A uses different exit  
125
4
P B uses different exit  
125

34. (iii) What is the probability that any of the four mice come out the
same exit and the other comes out a different exit?
4
P D uses different exit  
4 125
 P A uses different exit  
125
4
P B uses different exit  
125
4
PC uses different exit  
125

35. (iii) What is the probability that any of the four mice come out the
same exit and the other comes out a different exit?
4
P D uses different exit  
4 125
 P A uses different exit  
125
4
P B uses different exit  
125
4
PC uses different exit  
125
4
 Pany mouse uses different exit   4 
125

36. (iii) What is the probability that any of the four mice come out the
same exit and the other comes out a different exit?
4
P D uses different exit  
4 125
 P A uses different exit  
125
4
P B uses different exit  
125
4
PC uses different exit  
125
4
 Pany mouse uses different exit   4 
125
16

125

37. (iv) What is the probability that no more than two mice come out the
same exit?

38. (iv) What is the probability that no more than two mice come out the
same exit?
Pno more than 2 use same exit   1  Pall same  P3 use same

39. (iv) What is the probability that no more than two mice come out the
same exit?
Pno more than 2 use same exit   1  Pall same  P3 use same
1 16
 1 
125 125

40. (iv) What is the probability that no more than two mice come out the
same exit?
Pno more than 2 use same exit   1  Pall same  P3 use same
1 16
 1 
125 125
108

125

41. Permutations

42. Permutations
A permutation is an ordered set of objects

43. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects

44. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects
(i.e. use all of the objects)

45. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects
(i.e. use all of the objects)
If we arrange n different objects in a line, the number of ways we
could arrange them are;

46. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects
(i.e. use all of the objects)
If we arrange n different objects in a line, the number of ways we
could arrange them are;
possibilities
for object 1
Number of Arrangements  n

47. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects
(i.e. use all of the objects)
If we arrange n different objects in a line, the number of ways we
could arrange them are;
possibilities
possibilities for object 2
for object 1
Number of Arrangements  n  n  1

48. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects
(i.e. use all of the objects)
If we arrange n different objects in a line, the number of ways we
could arrange them are;
possibilities
possibilities for object 2 possibilities
for object 1 for object 3
Number of Arrangements  n  n  1  n  2 

49. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects
(i.e. use all of the objects)
If we arrange n different objects in a line, the number of ways we
could arrange them are;
possibilities
possibilities for object 2 possibilities possibilities
for object 1 for object 3
for last object
Number of Arrangements  n  n  1  n  2    1

50. Permutations
A permutation is an ordered set of objects
Case 1: Ordered Sets of n Different Objects, from a Set of n Such
Objects
(i.e. use all of the objects)
If we arrange n different objects in a line, the number of ways we
could arrange them are;
possibilities
possibilities for object 2 possibilities possibilities
for object 1 for object 3
for last object
Number of Arrangements  n  n  1  n  2    1
 n!

51. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?

52. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9!

53. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
gender does not matter

54. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
 362880 gender does not matter

55. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
 362880 gender does not matter
(ii) boys and girls alternate?

56. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
 362880 gender does not matter
(ii) boys and girls alternate?
(ALWAYS look after any restrictions first)

57. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
 362880 gender does not matter
(ii) boys and girls alternate?
(ALWAYS look after any restrictions first)
first person MUST
be a boy
Arrangements  1

58. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
 362880 gender does not matter
(ii) boys and girls alternate?
(ALWAYS look after any restrictions first)
first person MUST number of ways of
be a boy arranging the boys
Arrangements  1  5!

59. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
 362880 gender does not matter
(ii) boys and girls alternate?
(ALWAYS look after any restrictions first)
first person MUST number of ways of
be a boy arranging the boys
 4! number of ways of
Arrangements  1  5!
arranging the girls

60. e.g. In how many ways can 5 boys and 4 girls be arranged in a line
if;
(i) there are no restrictions?
Arrangements  9! With no restrictions, arrange 9 people
 362880 gender does not matter
(ii) boys and girls alternate?
(ALWAYS look after any restrictions first)
first person MUST number of ways of
be a boy arranging the boys
 4! number of ways of
Arrangements  1  5!
 2880 arranging the girls

61. (iii) What is the probability of the boys and girls alternating?

62. (iii) What is the probability of the boys and girls alternating?
2880
Pboys & girls alternate 
362880

63. (iii) What is the probability of the boys and girls alternating?
2880
Pboys & girls alternate 
362880
1

126

64. (iii) What is the probability of the boys and girls alternating?
2880
Pboys & girls alternate 
362880
1

126
(iv) Two girls wish to be together?

65. (iii) What is the probability of the boys and girls alternating?
2880
Pboys & girls alternate 
362880
1

126
(iv) Two girls wish to be together?
the number of ways the
girls can be arranged
Arrangements  2!

66. (iii) What is the probability of the boys and girls alternating?
2880
Pboys & girls alternate 
362880
1

126
(iv) Two girls wish to be together?
the number of ways the
number of ways of
girls can be arranged
arranging 8 objects
Arrangements  2!  8! (2 girls)  7 others

67. (iii) What is the probability of the boys and girls alternating?
2880
Pboys & girls alternate 
362880
1

126
(iv) Two girls wish to be together?
the number of ways the
number of ways of
girls can be arranged
arranging 8 objects
Arrangements  2!  8! (2 girls)  7 others
 80640

68. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)

69. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)

70. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;

71. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;
possibilities
for object 1
Number of Arrangements  n

72. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;
possibilities
possibilities for object 2
for object 1
Number of Arrangements  n  n  1

73. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;
possibilities
possibilities for object 2 possibilities
for object 1 for object 3
Number of Arrangements  n  n  1  n  2 

74. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;
possibilities
possibilities for object 2 possibilities possibilities
for object 1 for object 3 for object k
Number of Arrangements  n  n  1  n  2    n  k  1

75. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;
possibilities
possibilities for object 2 possibilities possibilities
for object 1 for object 3 for object k
Number of Arrangements  n  n  1  n  2    n  k  1
n  k n  k  1321
 nn  1n  2 n  k  1 
n  k n  k  1321

76. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;
possibilities
possibilities for object 2 possibilities possibilities
for object 1 for object 3 for object k
Number of Arrangements  n  n  1  n  2    n  k  1
n  k n  k  1321
 nn  1n  2 n  k  1 
n  k n  k  1321
n!

n  k !

77. Case 2: Ordered Sets of k Different Objects, from a Set of n Such
Objects (k < n)
(i.e. use some of the objects)
If we have n different objects in a line, but only want to arrange k of
them, the number of ways we could arrange them are;
possibilities
possibilities for object 2 possibilities possibilities
for object 1 for object 3 for object k
Number of Arrangements  n  n  1  n  2    n  k  1
n  k n  k  1321
 nn  1n  2 n  k  1 
n  k n  k  1321
n!

n  k !
 nPk

78. e.g. (i) From the letters of the word PROBLEMS how many 5
letter words are possible if;
a) there are no restrictions?

79. e.g. (i) From the letters of the word PROBLEMS how many 5
letter words are possible if;
a) there are no restrictions?
Words 8P5

80. e.g. (i) From the letters of the word PROBLEMS how many 5
letter words are possible if;
a) there are no restrictions?
Words 8P5
 6720

81. e.g. (i) From the letters of the word PROBLEMS how many 5
letter words are possible if;
a) there are no restrictions?
Words 8P5
 6720
b) they must begin with P?

82. e.g. (i) From the letters of the word PROBLEMS how many 5
letter words are possible if;
a) there are no restrictions?
Words 8P5
 6720
b) they must begin with P?
the number of ways P
can be placed first
Words  1

83. e.g. (i) From the letters of the word PROBLEMS how many 5
letter words are possible if;
a) there are no restrictions?
Words 8P5
 6720
b) they must begin with P?
the number of ways P
Question now becomes
can be placed first
how many 4 letter words
Words  1 7 P4 ROBLEMS

84. e.g. (i) From the letters of the word PROBLEMS how many 5
letter words are possible if;
a) there are no restrictions?
Words 8P5
 6720
b) they must begin with P?
the number of ways P
Question now becomes
can be placed first
how many 4 letter words
Words  1 7 P4 ROBLEMS
 840

85. c) P is included, but not at the beginning, and M is excluded?

86. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
can be placed in
Words  4

87. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES

88. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440

89. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?

90. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6

91. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6
 20160

92. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6
 20160
Ways Bill & Ted
can go
Ways (restrictions)  4P2

93. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6
 20160
Ways Bill & Ted Ways Greg
can go can go
Ways (restrictions)  4P2 4 P1

94. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6
 20160
Ways Bill & Ted Ways Greg
can go can go
Ways (restrictions)  4P2 4 P 5 P3
1
Ways remaining
people can go

95. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6
 20160
Ways Bill & Ted Ways Greg
can go can go
Ways (restrictions)  4P2 4 P 5 P3
1
Ways remaining
 2880 people can go

96. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6 2880
 20160 PB & T left, G right  
20160
Ways Bill & Ted Ways Greg
can go can go
Ways (restrictions)  4P2 4 P 5 P3
1
Ways remaining
 2880 people can go

97. c) P is included, but not at the beginning, and M is excluded?
the number of positions P
Question now becomes
can be placed in
how many 4 letter words
Words  4 6 P4 ROBLES
 1440
(ii) Six people are in a boat with eight seats, for on each side.
What is the probability that Bill and Ted are on the left side and
Greg is on the right?
Ways (no restrictions) 8P6 2880
 20160 PB & T left, G right  
20160
Ways Bill & Ted Ways Greg 1
can go can go 
7
Ways (restrictions)  4P2 4 P 5 P3
1
Ways remaining
 2880 people can go

98. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.

99. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?

100. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3

101. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60

102. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?

103. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2

104. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20

105. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3

106. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3  60

107. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3  60
4 block Towers  5P4

108. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3  60
4 block Towers  5P4  120

109. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3  60
4 block Towers  5P4  120
5 block Towers  5P5

110. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3  60
4 block Towers  5P4  120
5 block Towers  5P5  120

111. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3  60
4 block Towers  5P4  120
5 block Towers  5P5  120
Total number of Towers  320

112. 2006 Extension 1 HSC Q3c)
Sophia has five coloured blocks: one red, one blue, one green, one
yellow and one white.
She stacks two, three, four or five blocks on top of one another to
form a vertical tower.
(i) How many different towers are there that she could form that are
three blocks high?
Towers  5P3
 60
(ii) How many different towers can she form in total?
2 block Towers  5P2  20
3 block Towers  5P3  60
4 block Towers  5P4  120 Exercise 10E; odd (not 39)
5 block Towers  5P5  120
Total number of Towers  320