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Probability HelpPrev TopicNext Topic
-
Hi guys if someone could help me understand this I would much appreciate it. Thanks
IF I WERE TO BET ON HEADS OR TAILS OR ANY GAME WITH ONLY 2 OPTIONS A OR B AND I WAS GUARANTEED TO WIN 5/8 HOW MANY SEGMENTS WOULD I NEED TO WIN A 5 LEG MULTI/PARLAY BET?
EXAMPLE A,A,A,A,A,B,B,B - B,B,B,A,A,A,A,A...
A IS OPTION 1 AND B IS OPTION 2...
HELP WOULD BE APPRECIATED.
THANKS
-
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,812 Posts
OfflineThere's a total of 56 possible combinations of 5 A's with 3 B's.
It can be calculated either with A's as 8 taken 5 at a time, or B's as 8 taken 3 at a time using the combinatorial function C(n, r) = n! / (r! · (n - r)!) where x! is the factorial defined as x! = x · (x - 1) · (x - 2) … 3 · 2 · 1 and 0! = 1.
A ways is C(8, 5) = 8! / (5! · (8 - 5)!) = 56
B ways is C(8, 3) = 8! / (3! · (8 - 3)!) = 56
The total possible ways of combining any set of A's and B's with 8 positions is 28 or 256.
There is also a symmetrical set of 3 A's with 5 B's that is exactly equal to 5 A's with 3 B's.
You can see the total and subsets below.
We highlighted your 5 A's and 3 B's red and its symmetrical counterpart 3 A's and 5 B's green.
Total
Subset
Combination
1
1
A
A
A
A
A
A
A
A
2
1
A
A
A
A
A
A
A
B
3
2
A
A
A
A
A
A
B
A
4
3
A
A
A
A
A
B
A
A
5
4
A
A
A
A
B
A
A
A
6
5
A
A
A
B
A
A
A
A
7
6
A
A
B
A
A
A
A
A
8
7
A
B
A
A
A
A
A
A
9
8
B
A
A
A
A
A
A
A
10
1
A
A
A
A
A
A
B
B
11
2
A
A
A
A
A
B
A
B
12
3
A
A
A
A
B
A
A
B
13
4
A
A
A
B
A
A
A
B
14
5
A
A
B
A
A
A
A
B
15
6
A
B
A
A
A
A
A
B
16
7
B
A
A
A
A
A
A
B
17
8
A
A
A
A
A
B
B
A
18
9
A
A
A
A
B
A
B
A
19
10
A
A
A
B
A
A
B
A
20
11
A
A
B
A
A
A
B
A
21
12
A
B
A
A
A
A
B
A
22
13
B
A
A
A
A
A
B
A
23
14
A
A
A
A
B
B
A
A
24
15
A
A
A
B
A
B
A
A
25
16
A
A
B
A
A
B
A
A
26
17
A
B
A
A
A
B
A
A
27
18
B
A
A
A
A
B
A
A
28
19
A
A
A
B
B
A
A
A
29
20
A
A
B
A
B
A
A
A
30
21
A
B
A
A
B
A
A
A
31
22
B
A
A
A
B
A
A
A
32
23
A
A
B
B
A
A
A
A
33
24
A
B
A
B
A
A
A
A
34
25
B
A
A
B
A
A
A
A
35
26
A
B
B
A
A
A
A
A
36
27
B
A
B
A
A
A
A
A
37
28
B
B
A
A
A
A
A
A
38
1
A
A
A
A
A
B
B
B
39
2
A
A
A
A
B
A
B
B
40
3
A
A
A
B
A
A
B
B
41
4
A
A
B
A
A
A
B
B
42
5
A
B
A
A
A
A
B
B
43
6
B
A
A
A
A
A
B
B
44
7
A
A
A
A
B
B
A
B
45
8
A
A
A
B
A
B
A
B
46
9
A
A
B
A
A
B
A
B
47
10
A
B
A
A
A
B
A
B
48
11
B
A
A
A
A
B
A
B
49
12
A
A
A
B
B
A
A
B
50
13
A
A
B
A
B
A
A
B
51
14
A
B
A
A
B
A
A
B
52
15
B
A
A
A
B
A
A
B
53
16
A
A
B
B
A
A
A
B
54
17
A
B
A
B
A
A
A
B
55
18
B
A
A
B
A
A
A
B
56
19
A
B
B
A
A
A
A
B
57
20
B
A
B
A
A
A
A
B
58
21
B
B
A
A
A
A
A
B
59
22
A
A
A
A
B
B
B
A
60
23
A
A
A
B
A
B
B
A
61
24
A
A
B
A
A
B
B
A
62
25
A
B
A
A
A
B
B
A
63
26
B
A
A
A
A
B
B
A
64
27
A
A
A
B
B
A
B
A
65
28
A
A
B
A
B
A
B
A
66
29
A
B
A
A
B
A
B
A
67
30
B
A
A
A
B
A
B
A
68
31
A
A
B
B
A
A
B
A
69
32
A
B
A
B
A
A
B
A
70
33
B
A
A
B
A
A
B
A
71
34
A
B
B
A
A
A
B
A
72
35
B
A
B
A
A
A
B
A
73
36
B
B
A
A
A
A
B
A
74
37
A
A
A
B
B
B
A
A
75
38
A
A
B
A
B
B
A
A
76
39
A
B
A
A
B
B
A
A
77
40
B
A
A
A
B
B
A
A
78
41
A
A
B
B
A
B
A
A
79
42
A
B
A
B
A
B
A
A
80
43
B
A
A
B
A
B
A
A
81
44
A
B
B
A
A
B
A
A
82
45
B
A
B
A
A
B
A
A
83
46
B
B
A
A
A
B
A
A
84
47
A
A
B
B
B
A
A
A
85
48
A
B
A
B
B
A
A
A
86
49
B
A
A
B
B
A
A
A
87
50
A
B
B
A
B
A
A
A
88
51
B
A
B
A
B
A
A
A
89
52
B
B
A
A
B
A
A
A
90
53
A
B
B
B
A
A
A
A
91
54
B
A
B
B
A
A
A
A
92
55
B
B
A
B
A
A
A
A
93
56
B
B
B
A
A
A
A
A
94
1
A
A
A
A
B
B
B
B
95
2
A
A
A
B
A
B
B
B
96
3
A
A
B
A
A
B
B
B
97
4
A
B
A
A
A
B
B
B
98
5
B
A
A
A
A
B
B
B
99
6
A
A
A
B
B
A
B
B
100
7
A
A
B
A
B
A
B
B
101
8
A
B
A
A
B
A
B
B
102
9
B
A
A
A
B
A
B
B
103
10
A
A
B
B
A
A
B
B
104
11
A
B
A
B
A
A
B
B
105
12
B
A
A
B
A
A
B
B
106
13
A
B
B
A
A
A
B
B
107
14
B
A
B
A
A
A
B
B
108
15
B
B
A
A
A
A
B
B
109
16
A
A
A
B
B
B
A
B
110
17
A
A
B
A
B
B
A
B
111
18
A
B
A
A
B
B
A
B
112
19
B
A
A
A
B
B
A
B
113
20
A
A
B
B
A
B
A
B
114
21
A
B
A
B
A
B
A
B
115
22
B
A
A
B
A
B
A
B
116
23
A
B
B
A
A
B
A
B
117
24
B
A
B
A
A
B
A
B
118
25
B
B
A
A
A
B
A
B
119
26
A
A
B
B
B
A
A
B
120
27
A
B
A
B
B
A
A
B
121
28
B
A
A
B
B
A
A
B
122
29
A
B
B
A
B
A
A
B
123
30
B
A
B
A
B
A
A
B
124
31
B
B
A
A
B
A
A
B
125
32
A
B
B
B
A
A
A
B
126
33
B
A
B
B
A
A
A
B
127
34
B
B
A
B
A
A
A
B
128
35
B
B
B
A
A
A
A
B
129
36
A
A
A
B
B
B
B
A
130
37
A
A
B
A
B
B
B
A
131
38
A
B
A
A
B
B
B
A
132
39
B
A
A
A
B
B
B
A
133
40
A
A
B
B
A
B
B
A
134
41
A
B
A
B
A
B
B
A
135
42
B
A
A
B
A
B
B
A
136
43
A
B
B
A
A
B
B
A
137
44
B
A
B
A
A
B
B
A
138
45
B
B
A
A
A
B
B
A
139
46
A
A
B
B
B
A
B
A
140
47
A
B
A
B
B
A
B
A
141
48
B
A
A
B
B
A
B
A
142
49
A
B
B
A
B
A
B
A
143
50
B
A
B
A
B
A
B
A
144
51
B
B
A
A
B
A
B
A
145
52
A
B
B
B
A
A
B
A
146
53
B
A
B
B
A
A
B
A
147
54
B
B
A
B
A
A
B
A
148
55
B
B
B
A
A
A
B
A
149
56
A
A
B
B
B
B
A
A
150
57
A
B
A
B
B
B
A
A
151
58
B
A
A
B
B
B
A
A
152
59
A
B
B
A
B
B
A
A
153
60
B
A
B
A
B
B
A
A
154
61
B
B
A
A
B
B
A
A
155
62
A
B
B
B
A
B
A
A
156
63
B
A
B
B
A
B
A
A
157
64
B
B
A
B
A
B
A
A
158
65
B
B
B
A
A
B
A
A
159
66
A
B
B
B
B
A
A
A
160
67
B
A
B
B
B
A
A
A
161
68
B
B
A
B
B
A
A
A
162
69
B
B
B
A
B
A
A
A
163
70
B
B
B
B
A
A
A
A
164
1
A
A
A
B
B
B
B
B
165
2
A
A
B
A
B
B
B
B
166
3
A
B
A
A
B
B
B
B
167
4
B
A
A
A
B
B
B
B
168
5
A
A
B
B
A
B
B
B
169
6
A
B
A
B
A
B
B
B
170
7
B
A
A
B
A
B
B
B
171
8
A
B
B
A
A
B
B
B
172
9
B
A
B
A
A
B
B
B
173
10
B
B
A
A
A
B
B
B
174
11
A
A
B
B
B
A
B
B
175
12
A
B
A
B
B
A
B
B
176
13
B
A
A
B
B
A
B
B
177
14
A
B
B
A
B
A
B
B
178
15
B
A
B
A
B
A
B
B
179
16
B
B
A
A
B
A
B
B
180
17
A
B
B
B
A
A
B
B
181
18
B
A
B
B
A
A
B
B
182
19
B
B
A
B
A
A
B
B
183
20
B
B
B
A
A
A
B
B
184
21
A
A
B
B
B
B
A
B
185
22
A
B
A
B
B
B
A
B
186
23
B
A
A
B
B
B
A
B
187
24
A
B
B
A
B
B
A
B
188
25
B
A
B
A
B
B
A
B
189
26
B
B
A
A
B
B
A
B
190
27
A
B
B
B
A
B
A
B
191
28
B
A
B
B
A
B
A
B
192
29
B
B
A
B
A
B
A
B
193
30
B
B
B
A
A
B
A
B
194
31
A
B
B
B
B
A
A
B
195
32
B
A
B
B
B
A
A
B
196
33
B
B
A
B
B
A
A
B
197
34
B
B
B
A
B
A
A
B
198
35
B
B
B
B
A
A
A
B
199
36
A
A
B
B
B
B
B
A
200
37
A
B
A
B
B
B
B
A
201
38
B
A
A
B
B
B
B
A
202
39
A
B
B
A
B
B
B
A
203
40
B
A
B
A
B
B
B
A
204
41
B
B
A
A
B
B
B
A
205
42
A
B
B
B
A
B
B
A
206
43
B
A
B
B
A
B
B
A
207
44
B
B
A
B
A
B
B
A
208
45
B
B
B
A
A
B
B
A
209
46
A
B
B
B
B
A
B
A
210
47
B
A
B
B
B
A
B
A
211
48
B
B
A
B
B
A
B
A
212
49
B
B
B
A
B
A
B
A
213
50
B
B
B
B
A
A
B
A
214
51
A
B
B
B
B
B
A
A
215
52
B
A
B
B
B
B
A
A
216
53
B
B
A
B
B
B
A
A
217
54
B
B
B
A
B
B
A
A
218
55
B
B
B
B
A
B
A
A
219
56
B
B
B
B
B
A
A
A
220
1
A
A
B
B
B
B
B
B
221
2
A
B
A
B
B
B
B
B
222
3
B
A
A
B
B
B
B
B
223
4
A
B
B
A
B
B
B
B
224
5
B
A
B
A
B
B
B
B
225
6
B
B
A
A
B
B
B
B
226
7
A
B
B
B
A
B
B
B
227
8
B
A
B
B
A
B
B
B
228
9
B
B
A
B
A
B
B
B
229
10
B
B
B
A
A
B
B
B
230
11
A
B
B
B
B
A
B
B
231
12
B
A
B
B
B
A
B
B
232
13
B
B
A
B
B
A
B
B
233
14
B
B
B
A
B
A
B
B
234
15
B
B
B
B
A
A
B
B
235
16
A
B
B
B
B
B
A
B
236
17
B
A
B
B
B
B
A
B
237
18
B
B
A
B
B
B
A
B
238
19
B
B
B
A
B
B
A
B
239
20
B
B
B
B
A
B
A
B
240
21
B
B
B
B
B
A
A
B
241
22
A
B
B
B
B
B
B
A
242
23
B
A
B
B
B
B
B
A
243
24
B
B
A
B
B
B
B
A
244
25
B
B
B
A
B
B
B
A
245
26
B
B
B
B
A
B
B
A
246
27
B
B
B
B
B
A
B
A
247
28
B
B
B
B
B
B
A
A
248
1
A
B
B
B
B
B
B
B
249
2
B
A
B
B
B
B
B
B
250
3
B
B
A
B
B
B
B
B
251
4
B
B
B
A
B
B
B
B
252
5
B
B
B
B
A
B
B
B
253
6
B
B
B
B
B
A
B
B
254
7
B
B
B
B
B
B
A
B
255
8
B
B
B
B
B
B
B
A
256
1
B
B
B
B
B
B
B
B
The One Over None
I Know...