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 ways of winning, and there are 9x8x7/3x2x1=84 ways of picking three numbers, so the odds are 8 in 84, about 10%.

Posted by Oskar on 2004-07-30 13:01:15