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 9!/((3!)*(9-3)!) = 84 combinations.

There are nine tic-tac-toe grid locations, with three ways of winning by row, three by column, and two by diagonal giving eight possible winning combinations.

The winning probability is then 8/84 = 2/21 =~ 0.095238095.

Posted by Dej Mar on 2008-03-05 21:08:30