

This is the game of "Noughts and Crosses" or "Tic Tac Toe".
In how many different ways can the first "X" and "O" be placed on the grid?
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There are nine different places the first "X" can be drawn. This leaves eight different places for the first "O" to be drawn.
The total number of different ways the first two symbols can be drawn is:
9 x 8 = 72
In how many different ways can the first three moves be placed on the grid?
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The javascript for this game above was kindly made public by Stephen Ostermiller (GNU General Public License as published by the Free Software Foundation) who also provides an excellent description of Tic-Tac-Toe Strategy.