1. PROBABILITY WORKSHOP with blocks
Hands-on Lwr. 2 nd’ry MATHS
PROBABILITY WORKSHOP with blocks
By Jon Molomby

2. Q : What is the waitress asking ?
Review of Terms : AND and OR
Q : What is the waitress asking ?

3. The waitress : “ Tea OR Coffee ? ”
Review of Terms : AND and OR
The waitress : “ Tea OR Coffee ? ”

4. A mathematician might say : “ ‘Tea OR Coffee ?’ …

5. … means Tea OR Coffee OR BOTH ”

6. … but Tea AND Coffee looks like this.

7. Do you mean Tea XOR Coffee
- not BOTH ? ”

8. The waitress : “ Yes , that’s what I mean ! Tea XOR Coffee ? ”

9. 1. Permutations 2. Combinations 3. Random Choice
We will look at PROBABILITY using 4 blocks
Green Blue Red Yellow
1. Permutations Combinations 3. Random Choice
You should have
4 blocks of different colour
download the worksheet from

10. Hands-on Lwr. 2 nd’ry MATHS1.
PERMUTATIONS
with

11. When Caleb Gattegno taught Permutations (in “Mathematics at your Fingertips” : ) he would ask students to make different carriages for a train using Cuisenaire rods

12. No. of different arrangements ?
Permutations
Green
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !

13. No. of different arrangements ?
Permutations
Green Blue
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !
2 (G & B )
( GB, BG )
2 !

14. No. of different arrangements ?
Permutations
Green Blue Red
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !
2 (G & B )
( GB, BG )
2 !
3 (G & B & R )
( GBR, GRB, BRG, BGR, RBG, RGB )
3 !

15. No. of different arrangements ?
Permutations
Green Blue Red Yellow
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !
2 (G & B )
( GB, BG )
2 !
3 (G & B & R )
( GBR, GRB, BRG, BGR, RBG, RGB )
3 !
4 (G & B & R & Y ) 24
4 !

16. No. of different arrangements ?
Permutations
Green Blue Red Yellow
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !
2 (G & B )
( GB, BG )
2 !
3 (G & B & R )
( GBR, GRB, BRG, BGR, RBG, RGB )
3 !
4 (G & B & R & Y ) 24
4 ! 5

17. No. of different arrangements ?
Permutations
Green Blue Red Yellow
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !
2 (G & B )
( GB, BG )
2 !
3 (G & B & R )
( GBR, GRB, BRG, BGR, RBG, RGB )
3 !
4 (G & B & R & Y ) 24
4 ! 5
120
5 !

18. No. of different arrangements ?
Permutations
Green Blue Red Yellow
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !
2 (G & B )
( GB, BG )
2 !
3 (G & B & R )
( GBR, GRB, BRG, BGR, RBG, RGB )
3 !
4 (G & B & R & Y ) 24
4 ! 5
120
5 ! 6

19. No. of different arrangements ?
Permutations
Green Blue Red Yellow
No. of “carriages”
No. of different arrangements ?
Simply expressed
1 (G )
( G )
1 !
2 (G & B )
( GB, BG )
2 !
3 (G & B & R )
( GBR, GRB, BRG, BGR, RBG, RGB )
3 !
4 (G & B & R & Y ) 24
4 ! 5
120
5 ! 6
720
6 !

20. n number of distinct things
Permutations
The General Rule
n number of distinct things
can be arranged in
n ! ways

21. 2) Four blocks (order important) ?
PERMUTATIONS with
2) Four blocks (order important) ?
Hint :
(remember Q.1) 

22. 2) Four blocks (order important) ?
PERMUTATIONS with
2) Four blocks (order important) ? 4 

23. 2) Four blocks (order important) ?
PERMUTATIONS with
2) Four blocks (order important) ?
4 x 3 

24. 2) Four blocks (order important) ?
PERMUTATIONS with
2) Four blocks (order important) ?
4 x 3 x 2 

25. 2) Four blocks (order important) ?
PERMUTATIONS with
2) Four blocks (order important) ?
4 x 3 x 2 x 1 

26. 2) Four blocks (order important) ?
PERMUTATIONS with
2) Four blocks (order important) ?
4 x 3 x 2 x = 24 

27. 2) Four blocks (order important) ?
PERMUTATIONS with
2) Four blocks (order important) ?
4 x 3 x 2 x = 24
Ans : 24 

28. 3) Red always first (order important) ?
PERMUTATIONS with
3) Red always first (order important) ? 

29. 3) Red always first (order important) ?
PERMUTATIONS with
3) Red always first (order important) ?
? ? ?
Red 

30. 3) Red always first (order important) ?
PERMUTATIONS with
3) Red always first (order important) ?
1 x ? ?
Red 

31. 3) Red always first (order important) ?
PERMUTATIONS with
3) Red always first (order important) ?
1 x 3 x ?
Red 

32. 3) Red always first (order important) ?
PERMUTATIONS with
3) Red always first (order important) ?
1 x 3 x 2 x = 6
Red
Ans : 6 

33. PERMUTATIONS with
4) Red not first ?
Hint :
(remember Q.3) 

34. PERMUTATIONS with 4) Red not first ? 
All possibilities minus red first 

35. PERMUTATIONS with 4) Red not first ? 
All possibilities minus red first (from Q.3) 

36. PERMUTATIONS with 4) Red not first ? 
All possibilities minus red first (from Q.3) = 

37. PERMUTATIONS with 4) Red not first ?  Ans : 18
All possibilities minus red first (from Q.3) =
Ans : 18 

38. PERMUTATIONS with
5) Yellow first or last ? 

39. PERMUTATIONS with 5) Yellow first or last ?  Mutually exclusive ,
so Yellow first plus Yellow last 

40. PERMUTATIONS with 5) Yellow first or last ? 6 + 6 = 12  Ans : 12
Mutually exclusive ,
so Yellow first plus Yellow last =
Ans : 12 

41. 6) Yellow neither first nor last ?
PERMUTATIONS with
6) Yellow neither first nor last ?
Hint :
(remember Q.5) 

42. 6) Yellow neither first nor last ?
PERMUTATIONS with
6) Yellow neither first nor last ?
All possibilities minus yellow first or last(from Q.5) 

43. 6) Yellow neither first nor last ?
PERMUTATIONS with
6) Yellow neither first nor last ?
All possibilities minus yellow first or last(from Q.5) 

44. 6) Yellow neither first nor last ?
PERMUTATIONS with
6) Yellow neither first nor last ?
All possibilities minus yellow first or last(from Q.5) 

45. 6) Yellow neither first nor last ?
PERMUTATIONS with
6) Yellow neither first nor last ?
All possibilities minus yellow first or last(from Q.5) =
Ans : 12 

46. PERMUTATIONS with
7) Red and Blue together ? 

47. PERMUTATIONS with
7) Red and Blue together ?
R B 

48. R B so 6 x 2! PERMUTATIONS with 7) Red and Blue together ?
x x = 6 BUT RB BR
R B so 6 x 2!
Ans : 12 

49. 8) Red and Blue never together ?
PERMUTATIONS with
8) Red and Blue never together ?
Hint :
(remember Q.7) 

50. 8) Red and Blue never together ?
PERMUTATIONS with
8) Red and Blue never together ?
All possibilities minus red and blue together
(from Q.7) 

51. 8) Red and Blue never together ?
PERMUTATIONS with
8) Red and Blue never together ?
All possibilities minus red and blue together
(from Q.7) =
Ans : 12 

52. Hint : PERMUTATIONS with
9) Red and Blue together, Red never next to Yellow ?
Hint :
(remember Q.7) 

53. 9) Red and Blue together, Red never next to Yellow ?
PERMUTATIONS with
9) Red and Blue together, Red never next to Yellow ?
Red and blue together minus yellow next to RB
(from Q7) (BRY or YRB) 

54. 9) Red and Blue together, Red never next to Yellow ?
PERMUTATIONS with
9) Red and Blue together, Red never next to Yellow ?
Red and blue together minus yellow next to RB
(from Q7) (BRY or YRB)
i.e. GBRY , GYRB
BRYG , YRBG 

55. 9) Red and Blue together, Red never next to Yellow ?
PERMUTATIONS with
9) Red and Blue together, Red never next to Yellow ?
Red and blue together minus yellow next to RB
(from Q7) (BRY or YRB)
i.e. GBRY , GYRB
BRYG , YRBG
= 8
Ans : 8 

56. 9) Red and Blue together, Red never next to Yellow ?
PERMUTATIONS with
9) Red and Blue together, Red never next to Yellow ?
Checking by listing all permutations :
RBGY RBYG RGBY RGYB RYBG RYGB
BRGY BRYG BGRY BGYR BYRG BYGR
GRBY GRYB GBRY GBYR GYRB GYBR
YRBG YRGB YBRG YBGR YGRB YGBR
Ans : 8 

57. 10) Red on one end AND Green the other
PERMUTATIONS with
10) Red on one end AND Green the other 

58. 10) Red on one end AND Green the other
PERMUTATIONS with
10) Red on one end AND Green the other
Like this : R _ _ G
R _ _ G
G _ _ R 

59. 10) Red on one end AND Green the other
PERMUTATIONS with
10) Red on one end AND Green the other
Possibilities : R B Y G
R Y B G
G B Y R
G Y B R
Ans : 

60. 10) Red on one end AND Green the other R B Y G R Y B G G B Y R G Y B R
PERMUTATIONS with
10) Red on one end AND Green the other
R B Y G
R Y B G
G B Y R
G Y B R
Ans : 4 

61. 10) Red on one end AND Green the other
PERMUTATIONS with
10) Red on one end AND Green the other
Checking by listing all permutations :
RBGY RBYG RGBY RGYB RYBG RYGB
BRGY BRYG BGRY BGYR BYRG BYGR
GRBY GRYB GBRY GBYR GYRB GYBR
YRBG YRGB YBRG YBGR YGRB YGBR
Ans : 4 

62. 11) Red on one end OR Green on an end
PERMUTATIONS with
11) Red on one end OR Green on an end 

63. 11) Red on one end OR Green on an end
PERMUTATIONS with
11) Red on one end OR Green on an end
Means Red on one end OR Green on an end or BOTH 

64. 11) Red on one end OR Green on an end
PERMUTATIONS with
11) Red on one end OR Green on an end
Means Red on one end OR Green on an end or BOTH
= All possibilities minus Red/Green in the middle 

65. 11) Red on one end OR Green on an end
PERMUTATIONS with
11) Red on one end OR Green on an end
Means Red on one end OR Green on an end or BOTH
= All possibilities minus Red/Green in the middle
i.e _ RG _ _ GR _
_ RG _ _ GR _ 

66. 11) Red on one end OR Green on an end
PERMUTATIONS with
11) Red on one end OR Green on an end
Means Red on one end OR Green on an end or BOTH
= All possibilities minus Red/Green in the middle
possibilities B RG Y B GR Y
Y RG B Y GR B 

67. 11) Red on one end OR Green on an end
PERMUTATIONS with
11) Red on one end OR Green on an end
Means Red on one end OR Green on an end or BOTH
= All possibilities minus Red/Green in the middle
possibilities B RG Y B GR Y
Y RG B Y GR B
= = 20
Ans : 20 

68. 11)Red on one end OR Green on an end or BOTH
PERMUTATIONS with
11)Red on one end OR Green on an end or BOTH
Checking by listing all permutations :
RBGY RBYG RGBY RGYB RYBG RYGB
BRGY BRYG BGRY BGYR BYRG BYGR
GRBY GRYB GBRY GBYR GYRB GYBR
YRBG YRGB YBRG YBGR YGRB YGBR
Ans : 20 

69. 12) Red on an end XOR Green on an end
PERMUTATIONS with
12) Red on an end XOR Green on an end 

70. 12) Red on an end XOR Green on an end
PERMUTATIONS with
12) Red on an end XOR Green on an end
Means Red on an end OR Green on an end
minus Red on an end AND Green on an end 

71. 12) Red on an end XOR Green on an end
PERMUTATIONS with
12) Red on an end XOR Green on an end
Means Red on an end OR Green on an end (Q.11)
minus Red on an end AND Green on an end (Q.10) 

72. 12) Red on an end XOR Green on an end
PERMUTATIONS with
12) Red on an end XOR Green on an end
Means Red on an end OR Green on an end (Q.11)
minus Red on an end AND Green on an end (Q.10) =
Ans : 16 

73. 12) Red on an end XOR Green on an end
PERMUTATIONS with
12) Red on an end XOR Green on an end
Checking by listing all permutations :
RBGY RBYG RGBY RGYB RYBG RYGB
BRGY BRYG BGRY BGYR BYRG BYGR
GRBY GRYB GBRY GBYR GYRB GYBR
YRBG YRGB YBRG YBGR YGRB YGBR
Ans : 16 

74. PERMUTATIONS with
13) Blocks in a circle 

75. Formula for things in a circle
PERMUTATIONS with
13) Blocks in a circle
Formula for things in a circle
= ( n – 1 ) ! 

76. PERMUTATIONS with 13) 4 Blocks in a circle = ( n – 1 ) !
Formula for things in a circle
= ( n – 1 ) !
So the number of blocks minus 1 factorial
= (4 – 1 )! = 3 !
Ans : 6 

77. the number of blocks factorial minus 1 = (4 – 1 )!
PERMUTATIONS with
13) Blocks in a circle
the number of blocks factorial minus 1 = (4 – 1 )!
Checking by listing all permutations :
Ans : 6 

78. Red and Blue not next to each other
PERMUTATIONS with
14) 4 Blocks in a circle :
Red and Blue not next to each other 

79. Red and Blue not next to each other
PERMUTATIONS with
14) 4 Blocks in a circle :
Red and Blue not next to each other
All ways in a circle minus Red/Blue together 

80. PERMUTATIONS with 14) 4 Blocks in a circle : 
Red and Blue not next to each other
All ways in a circle minus Red/Blue together
3 ! ! 2 !
= – = 2
Ans : 2 

81. Red and Blue not next to each other
PERMUTATIONS with
14) 4 Blocks in a circle :
Red and Blue not next to each other
Checking by listing all permutations :
Let 1 = Red and 2 = Blue
Ans : 2 

82. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)? 

83. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS : 

84. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS : 

85. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS :
4P2 = 

86. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS :
4P2 = 

87. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS :
4P2 =
Ans : 12 

88. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
An easier way ? 

89. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
An easier way ? Yes
Based on nPk = n factorial to the first k no. of factors 

90. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
An easier way ?
Based on nPk = n factorial to the first k no. of factors
4P2 = 4 factorial to the first two factors 

91. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
An easier way ?
Based on nPk = n factorial to the first k no. of factors
4P2 = 4 factorial to the first two factors
4 x = 12 

92. 15) 2 selected from 4 blocks (order important)?
PERMUTATIONS with
15) selected from 4 blocks (order important)?
An easier way ?
Based on nPk = n factorial to the first k no. of factors
4P2 = 4 factorial to the first two factors
4 x = 12
Ans : 12 

93. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)? 

94. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS : 

95. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS : 

96. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS :
4P3 = 

97. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS :
4P3 = 

98. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
Using the formula for PERMUTATIONS :
4P3 =
Ans : 24 

99. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
An easier way ? 

100. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
An easier way ? Yes
Based on nPk = n factorial to the first k no. of factors 

101. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
An easier way ?
Based on nPk = n factorial to the first k no. of factors
4P3 = 4 factorial to the first three factors 

102. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
An easier way ?
Based on nPk = n factorial to the first k no. of factors
4P3 = 4 factorial to the first three factors
4 x x = 

103. 16) 3 selected from 4 blocks (order important)?
PERMUTATIONS with
16) selected from 4 blocks (order important)?
An easier way ?
Based on nPk = n factorial to the first k no. of factors
4P3 = 4 factorial to the first three factors
4 x x = 24
Ans : 24 

104. Hands-on Lwr. 2 nd’ry MATHS2.
COMBINATIONS
with

105. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)? 

106. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
Using the formula for Combinations : 

107. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
Using the formula for Combinations : 

108. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
Using the formula for Combinations : 

109. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
Using the formula for Combinations :
Ans : 6 

110. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? 

111. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? Yes … Using Pascal’s Triangle 

112. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? Using Pascal’s Triangle 

113. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? Using Pascal’s Triangle 

114. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

115. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

116. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

117. 17) 2 chosen from 4 blocks (order not important)?
COMBINATIONS with
17) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle
Ans : 6 

118. 18) 3 chosen from 4 blocks (order not important)?
COMBINATIONS with
18) chosen from 4 blocks (order not important)?
An easier way ? Using Pascal’s Triangle 

119. 18) 3 chosen from 4 blocks (order not important)?
COMBINATIONS with
18) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

120. 18) 3 chosen from 4 blocks (order not important)?
COMBINATIONS with
18) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

121. 18) 3 chosen from 4 blocks (order not important)?
COMBINATIONS with
18) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

122. 18) 3 chosen from 4 blocks (order not important)?
COMBINATIONS with
18) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle
Ans : 4 

123. 19) 4 chosen from 4 blocks (order not important)?
COMBINATIONS with
19) chosen from 4 blocks (order not important)?
An easier way ? Using Pascal’s Triangle 

124. 19) 4 chosen from 4 blocks (order not important)?
COMBINATIONS with
19) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

125. 19) 4 chosen from 4 blocks (order not important)?
COMBINATIONS with
19) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

126. 19) 4 chosen from 4 blocks (order not important)?
COMBINATIONS with
19) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle
Ans : 1 

127. 20) 0 chosen from 4 blocks (order not important)?
COMBINATIONS with
20) chosen from 4 blocks (order not important)?
An easier way ? Using Pascal’s Triangle 

128. 20) 0 chosen from 4 blocks (order not important)?
COMBINATIONS with
20) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

129. 20) 0 chosen from 4 blocks (order not important)?
COMBINATIONS with
20) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

130. 20) 0 chosen from 4 blocks (order not important)?
COMBINATIONS with
20) chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle
Ans : 1 

131. 21) 1 chosen from 4 blocks (order not important)?
COMBINATIONS with
21) 1 chosen from 4 blocks (order not important)?
An easier way ? Using Pascal’s Triangle 

132. 21) 1 chosen from 4 blocks (order not important)?
COMBINATIONS with
21) 1 chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

133. 21) 1 chosen from 4 blocks (order not important)?
COMBINATIONS with
21) 1 chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle 

134. 21) 1 chosen from 4 blocks (order not important)?
COMBINATIONS with
21) 1 chosen from 4 blocks (order not important)?
An easier way ? 4C Using Pascal’s Triangle
Ans : 4 

135. Another handy trick with Combinations
COMBINATIONS with
Another handy trick with Combinations
nCr = nCn-r
e.g. 20C18 = 20C2 

136. Hands-on Lwr. 2 nd’ry MATHS
3. Random Choice
without replacement

137. RANDOM CHOICE with Put the 4 blocks inside your hands : 
What are the chances
if taken at random
…. ? 

138. RANDOM CHOICE with Put the 4 blocks inside your hands : 22)  Red
(taking 1) 

139. RANDOM CHOICE with Ans : 1 out of 4 Put the 4 blocks
inside your hands :
22)
Red
(taking 1)
Ans : 1 out of 4 

140. RANDOM CHOICE with Put the 4 blocks inside your hands : 23) 
Red or Blue
(taking 1) 

141. RANDOM CHOICE with Ans : 2 out of 4 = 1 out of 2 Put the 4 blocks
inside your hands :
23)
Red or Blue
(taking 1)
Ans : 2 out of 4 = 1 out of 2 

142. RANDOM CHOICE with Put the 4 blocks inside your hands : 24) 
Red then Blue
(taking 2
without replacement) 

143. RANDOM CHOICE with Ans : 𝟏 𝟒 × 𝟏 𝟑 = 𝟏 𝟏𝟐 = 1 out of 12
Put the 4 blocks
inside your hands :
24)
Red then Blue
(taking 2
without replacement)
Ans : 𝟏 𝟒 × 𝟏 𝟑 = 𝟏 𝟏𝟐 = 1 out of 12 

144. RANDOM CHOICE with Put 8 blocks inside your hands : 25)  Red
(taking 1) 

145. RANDOM CHOICE with Ans : 2 out of 8 = 1 out of 4 Put 8 blocks
inside your hands :
25)
Red
(taking 1)
Ans : 2 out of 8 = 1 out of 4 

146. RANDOM CHOICE with Put 8 blocks inside your hands : 26) 
Blue or Green
(taking 1) 

147. RANDOM CHOICE with Ans : 4 out of 8 = 1 out of 2 Put 8 blocks
inside your hands :
26)
Blue or Green
(taking 1)
Ans : 4 out of 8 = 1 out of 2 

148. RANDOM CHOICE with Put 8 blocks inside your hands : 27)  Blue, Blue
(taking 2
without replacement) 

149. RANDOM CHOICE with Ans : 𝟏 𝟒 × 𝟏 𝟕 = 𝟏 𝟐𝟖 1 out of 28 Put 8 blocks
inside your hands :
27)
Blue, Blue
(taking 2
without replacement)
Ans : 𝟏 𝟒 × 𝟏 𝟕 = 𝟏 𝟐𝟖 out of 28 

150. RANDOM CHOICE with Put 8 blocks inside your hands : 28) 
Any 2 of the same
colour (taking 2
without replacement) 

151. RANDOM CHOICE with Ans : 𝟏× 𝟏 𝟕 = 𝟏 𝟕 1 out of 7 Put 8 blocks
inside your hands :
28)
Any 2 of the same
colour (taking 2
without replacement)
Ans : 𝟏× 𝟏 𝟕 = 𝟏 𝟕 out of 7 

152. RANDOM CHOICE with Put 8 blocks inside your hands : 29) 
Any 2 of different
colour (taking 2
without replacement) 

153. RANDOM CHOICE with Ans : 𝟏× 𝟔 𝟕 = 𝟔 𝟕 6 out of 7 Put 8 blocks
inside your hands :
29)
Any 2 of different
colour (taking 2
without replacement)
Ans : 𝟏× 𝟔 𝟕 = 𝟔 𝟕 out of 7 

154. Permutation question : How many ways can you order
PERMUTATIONS with
30)
Permutation question :
How many ways can you order
8 blocks if there are
2 red, 2 blue, 2 yellow, 2 green ? 

155. Permutation question : How many ways can you order
PERMUTATIONS with
30)
Permutation question :
How many ways can you order
8 blocks if there are
2 red, 2 blue, 2 yellow, 2 green ?
Ans : 8! / (2! 2! 2! 2!) = 2520 ways 

156. PERMUTATIONS with 31) 8 blocks in a circle if there are 
Permutation question :
How many ways can you order
8 blocks in a circle if there are
2 red, 2 blue, 2 yellow, 2 green ? 

157. PERMUTATIONS with 31) Ans : 7! / (2! 2! 2! 2!) = 315 ways
Permutation question :
How many ways can you order
8 blocks in a circle if there are
2 red, 2 blue, 2 yellow, 2 green ?
Ans : 7! / (2! 2! 2! 2!) = 315 ways 

158. PERMUTATIONS with 32) 2 blocks (order is important) from 5 blocks
32)  
Permutation question :
How many ways can you select
2 blocks (order is important) from 5 blocks
(green, green, blue, red, yellow)
[note : 5P2 over 2 ! is not correct]

159. Ans : 4P2 + 1 = 13 (see next slide)
PERMUTATIONS with
32)  
Permutation question :
How many ways can you select
2 blocks (order is important) from 5 blocks
(green, green, blue, red, yellow)
[note : 5P2 over 2 ! is not correct]
Ans : 4P = (see next slide)

160. PERMUTATIONS with
32)  There is no difference between Green 1 and Green 2 So the permutations are : GB, GR, GY,
BR, BG, BY,
RG, RY, RB,
YG, YB, YR. i.e. 4P2 = 12
+ GG
Ans :

161. 33) Some groups have 4 blocks,
COMBINATIONS
33)   Some groups have 4 blocks,
and some groups have 4 triangular prisms.
In how many ways
can I choose one block and one triangular prism ?

162. 33) Some groups have 4 blocks,
COMBINATIONS with
33)   Some groups have 4 blocks,
and some groups have 4 triangular prisms.
In how many ways
can I choose one block and one triangular prism ?
Ans : ways (see next slide)

163. 33) Based on the Fundamental Counting Principle
COMBINATIONS
33)   Based on the Fundamental Counting Principle
If I have m kind of things and n kind of things,
I can combine one of each in m x n ways
4 blocks x 4 triangular prisms = 16 ways
Ans : 16 ways

164. LINKS Maths with Geoboards Lower Secondary Maths Hands on
My Youtube channel : “ Maths with Geoboards “ ( for videos )
My website :
( for worksheets ) My
( for contact )
=========================================================================================================

165. Youtube Channel : “ Maths with Geoboards” videos so far
Pythagoras’ Theorem
Pythagoras Theorem Vol. 1
Pythagoras Theorem Vol. 2
Proofs of Pythagoras Theorem - Geometric
Proofs of Pythagoras Theorem - Algebraic
Number Theory
Prime Numbers
Fibonacci Numbers
Factors and Multiples
General
How to Make Geo-boards
Angles
Introductory Terms
Easy Angle Problems
The World’s Two Hardest Easy Geometry Problems
Indices
Indices : Laws 1, 2, 3 and 4
Indices : Word Problems
Probability
The Monty Hall Problem
Use Geoboards
Worksheet Videos
Worksheet Videos
Use Geoboards
Worksheet Videos

166. THE END

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