If I put nine pieces of paper, with a digit from 1-9 written on each one, into a hat, and pull 3 out without replacement, what is the likelihood that I will select three numbers that result in a winning tic-tac-toe?
1 | 2 | 3
---+---+---
4 | 5 | 6
---+---+---
7 | 8 | 9
There are only 8 different ways to win at tic-tac-toe...
- 123
- 456
- 789
- 147
- 258
- 369
- 159
- 753
and there are 84 different way you can pick 3 out of 9 numbers. (I don't know what the formula is, but I counted them)
- 123
- 124
- 125
- 126
- 127
- 128
- 129
- 134
- 135
- 136
- 137
- 138
- 139
- 145
- 146
- 147
- 148
- 149
- 156
- 157
- 158
- 159
- 167
- 168
- 169
- 178
- 179
- 189
- 234
- 235
- 236
- 237
- 238
- 239
- 245
- 246
- 247
- 248
- 249
- 256
- 257
- 258
- 259
- 267
- 268
- 269
- 278
- 279
- 289
- 345
- 346
- 347
- 348
- 349
- 356
- 357
- 358
- 359
- 367
- 368
- 369
- 378
- 379
- 389
- 456
- 457
- 458
- 459
- 467
- 468
- 469
- 478
- 479
- 489
- 567
- 568
- 569
- 578
- 579
- 589
- 678
- 679
- 689
- 789
So the answer is 8/84 or about 9.5%.
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Posted by Danny
on 2004-07-30 13:08:34 |
order doesn't matter
