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 

(In reply to re: Answer by Juggler)

Your interesting method of calculating gives (24+16+8)/(9*8*7)=6/63 and this is exactly equal to the answer, 8/84, that others obtained by observing that there are 3 rows, 3 columns, and 2 diagonals for a total of 8 3-element subsets of {1,2,...,9} that "win" out of the possible (9 choose 3)=84 3-element subsets of {1,2,...,9}. Your decimal arithmetic is a little off, however. 6/63=8/84=.095238092358092358...=95238/999999, which disagrees significantly with .09524192.  I point this out because it was unclear to me whether or not you were claiming that earlier answers of 8/84 were incorrect, which they are not. 

Posted by Richard on 2004-07-30 23:41:17