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 8 different winning lines which can be made, each line can be completed in any one of 6 ways. The total combination of winning ways is 48. The total number of ways in which 3 selections can be made from 9 is 9!/(9-3)! = 504. The answer is therefore 84/8

Posted by Mark on 2004-10-04 09:05:19