Exercise-1
expand.grid(Coin=c("Head","Tail"),Dice=c(1:6))
Coin Dice
1 Head 1
2 Tail 1
3 Head 2
4 Tail 2
5 Head 3
6 Tail 3
7 Head 4
8 Tail 4
9 Head 5
10 Tail 5
11 Head 6
12 Tail 6
Exercise-2
a <- c(1:10); names(a) <- a
a %o% a
1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100
Exercise-3
values <- c("A", 2, 3, 4, 5, 6, 7, 8, 9, 10, "J", "Q", "K")
suits <- c("d", "c", "s", "h")
d <- expand.grid(values,suits)
deck <- matrix(paste0(d[,1],d[,2]),ncol = 4)
colnames(deck)<-c("Diamonds","Clubs ","Spades ","Hearths ")
rownames(deck)<-values
deck
Diamonds Clubs Spades Hearths
A "Ad" "Ac" "As" "Ah"
2 "2d" "2c" "2s" "2h"
3 "3d" "3c" "3s" "3h"
4 "4d" "4c" "4s" "4h"
5 "5d" "5c" "5s" "5h"
6 "6d" "6c" "6s" "6h"
7 "7d" "7c" "7s" "7h"
8 "8d" "8c" "8s" "8h"
9 "9d" "9c" "9s" "9h"
10 "10d" "10c" "10s" "10h"
J "Jd" "Jc" "Js" "Jh"
Q "Qd" "Qc" "Qs" "Qh"
K "Kd" "Kc" "Ks" "Kh"
Exercise-4
Solution-1
dim(combn(52,5))
[1] 5 2598960
Solution-2
choose(52,5)
[1] 2598960
Solution-3
#Molly Renaud
starting_hands = combn(52, 5, FUN = NULL, simplify = FALSE)
length(starting_hands)
[1] 2598960
Exercise-5
colors <- c("red", "blue", "green", "white", "black", "yellow")
combn(colors,3,simplify = TRUE)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] "red" "red" "red" "red" "red" "red" "red" "red"
[2,] "blue" "blue" "blue" "blue" "green" "green" "green" "white"
[3,] "green" "white" "black" "yellow" "white" "black" "yellow" "black"
[,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
[1,] "red" "red" "blue" "blue" "blue" "blue" "blue" "blue"
[2,] "white" "black" "green" "green" "green" "white" "white" "black"
[3,] "yellow" "yellow" "white" "black" "yellow" "black" "yellow" "yellow"
[,17] [,18] [,19] [,20]
[1,] "green" "green" "green" "white"
[2,] "white" "white" "black" "black"
[3,] "black" "yellow" "yellow" "yellow"
Exercise-6
colors <- c("red", "blue", "green", "white", "black", "yellow")
combn(colors[order(colors)],3)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] "black" "black" "black" "black" "black" "black" "black" "black"
[2,] "blue" "blue" "blue" "blue" "green" "green" "green" "red"
[3,] "green" "red" "white" "yellow" "red" "white" "yellow" "white"
[,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
[1,] "black" "black" "blue" "blue" "blue" "blue" "blue" "blue"
[2,] "red" "white" "green" "green" "green" "red" "red" "white"
[3,] "yellow" "yellow" "red" "white" "yellow" "white" "yellow" "yellow"
[,17] [,18] [,19] [,20]
[1,] "green" "green" "green" "red"
[2,] "red" "red" "white" "white"
[3,] "white" "yellow" "yellow" "yellow"
Exercise-7
colors <- c("red", "blue", "green", "white", "black", "yellow")
expand.grid(colors,colors,colors)
Var1 Var2 Var3
1 red red red
2 blue red red
3 green red red
4 white red red
5 black red red
6 yellow red red
7 red blue red
8 blue blue red
9 green blue red
10 white blue red
11 black blue red
12 yellow blue red
13 red green red
14 blue green red
15 green green red
16 white green red
17 black green red
18 yellow green red
19 red white red
20 blue white red
21 green white red
22 white white red
23 black white red
24 yellow white red
25 red black red
26 blue black red
27 green black red
28 white black red
29 black black red
30 yellow black red
31 red yellow red
32 blue yellow red
33 green yellow red
34 white yellow red
35 black yellow red
36 yellow yellow red
37 red red blue
38 blue red blue
39 green red blue
40 white red blue
41 black red blue
42 yellow red blue
43 red blue blue
44 blue blue blue
45 green blue blue
46 white blue blue
47 black blue blue
48 yellow blue blue
49 red green blue
50 blue green blue
51 green green blue
52 white green blue
53 black green blue
54 yellow green blue
55 red white blue
56 blue white blue
57 green white blue
58 white white blue
59 black white blue
60 yellow white blue
61 red black blue
62 blue black blue
63 green black blue
64 white black blue
65 black black blue
66 yellow black blue
67 red yellow blue
68 blue yellow blue
69 green yellow blue
70 white yellow blue
71 black yellow blue
72 yellow yellow blue
73 red red green
74 blue red green
75 green red green
76 white red green
77 black red green
78 yellow red green
79 red blue green
80 blue blue green
81 green blue green
82 white blue green
83 black blue green
84 yellow blue green
85 red green green
86 blue green green
87 green green green
88 white green green
89 black green green
90 yellow green green
91 red white green
92 blue white green
93 green white green
94 white white green
95 black white green
96 yellow white green
97 red black green
98 blue black green
99 green black green
100 white black green
101 black black green
102 yellow black green
103 red yellow green
104 blue yellow green
105 green yellow green
106 white yellow green
107 black yellow green
108 yellow yellow green
109 red red white
110 blue red white
111 green red white
112 white red white
113 black red white
114 yellow red white
115 red blue white
116 blue blue white
117 green blue white
118 white blue white
119 black blue white
120 yellow blue white
121 red green white
122 blue green white
123 green green white
124 white green white
125 black green white
126 yellow green white
127 red white white
128 blue white white
129 green white white
130 white white white
131 black white white
132 yellow white white
133 red black white
134 blue black white
135 green black white
136 white black white
137 black black white
138 yellow black white
139 red yellow white
140 blue yellow white
141 green yellow white
142 white yellow white
143 black yellow white
144 yellow yellow white
145 red red black
146 blue red black
147 green red black
148 white red black
149 black red black
150 yellow red black
151 red blue black
152 blue blue black
153 green blue black
154 white blue black
155 black blue black
156 yellow blue black
157 red green black
158 blue green black
159 green green black
160 white green black
161 black green black
162 yellow green black
163 red white black
164 blue white black
165 green white black
166 white white black
167 black white black
168 yellow white black
169 red black black
170 blue black black
171 green black black
172 white black black
173 black black black
174 yellow black black
175 red yellow black
176 blue yellow black
177 green yellow black
178 white yellow black
179 black yellow black
180 yellow yellow black
181 red red yellow
182 blue red yellow
183 green red yellow
184 white red yellow
185 black red yellow
186 yellow red yellow
187 red blue yellow
188 blue blue yellow
189 green blue yellow
190 white blue yellow
191 black blue yellow
192 yellow blue yellow
193 red green yellow
194 blue green yellow
195 green green yellow
196 white green yellow
197 black green yellow
198 yellow green yellow
199 red white yellow
200 blue white yellow
201 green white yellow
202 white white yellow
203 black white yellow
204 yellow white yellow
205 red black yellow
206 blue black yellow
207 green black yellow
208 white black yellow
209 black black yellow
210 yellow black yellow
211 red yellow yellow
212 blue yellow yellow
213 green yellow yellow
214 white yellow yellow
215 black yellow yellow
216 yellow yellow yellow
Exercise-8 & 9
#Quantity:
total <- choose(3,1)+choose(3,2)+choose(3,3)
total
[1] 7
#List:
colors <- c("red", "blue", "green", "white", "black", "yellow")
clist <- list(combn(colors,1),combn(colors,2),combn(colors,3))
clist
[[1]]
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] "red" "blue" "green" "white" "black" "yellow"
[[2]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] "red" "red" "red" "red" "red" "blue" "blue" "blue"
[2,] "blue" "green" "white" "black" "yellow" "green" "white" "black"
[,9] [,10] [,11] [,12] [,13] [,14] [,15]
[1,] "blue" "green" "green" "green" "white" "white" "black"
[2,] "yellow" "white" "black" "yellow" "black" "yellow" "yellow"
[[3]]
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] "red" "red" "red" "red" "red" "red" "red" "red"
[2,] "blue" "blue" "blue" "blue" "green" "green" "green" "white"
[3,] "green" "white" "black" "yellow" "white" "black" "yellow" "black"
[,9] [,10] [,11] [,12] [,13] [,14] [,15] [,16]
[1,] "red" "red" "blue" "blue" "blue" "blue" "blue" "blue"
[2,] "white" "black" "green" "green" "green" "white" "white" "black"
[3,] "yellow" "yellow" "white" "black" "yellow" "black" "yellow" "yellow"
[,17] [,18] [,19] [,20]
[1,] "green" "green" "green" "white"
[2,] "white" "white" "black" "black"
[3,] "black" "yellow" "yellow" "yellow"
Exercise-10
Solution-1
c4 <- choose(4,1)+choose(4,2)+choose(4,3)+choose(4,4)
c6 <- choose(6,1)+choose(6,2)+choose(6,3)+choose(6,4)+choose(6,5)
c8 <- choose(8,1)+choose(8,2)+choose(8,3)+choose(8,4)+choose(8,5)
ctotal <- c4 + c6 + c8
ctotal
## [1] 295
Solution-2
ctotal = 0
i = 0
for (i in c(4,6,8))
{
c <- choose(i,1)+choose(i,2)+choose(i,3)+choose(i,4)+choose(i,5)
str1 <- paste("For",i,"colour pallet > Number of combinations:",c,sep = " ")
print(str1)
ctotal <- ctotal + c
}
## [1] "For 4 colour pallet > Number of combinations: 15"
## [1] "For 6 colour pallet > Number of combinations: 62"
## [1] "For 8 colour pallet > Number of combinations: 218"
str2 <- paste("Total number of combinations:",ctotal)
print(str2)
## [1] "Total number of combinations: 295"