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%.

Posted by Danny on 2004-07-30 13:08:34