Tictactoe probability?

Question

-confused-

http://www.btinternet.com/~se16/hgb/tictactoe.htm
this website supplies all the answers I need but I don't understand them! can someone please help me?

thanks (:

i dont understand the formula
"
Slightly harder:there are again 8 lines of three squares, and it doesn't matter in which order the three Os were placed, and the three Xs could have gone into three of the other six squares in any order (providing that the Xs are not three in a row). Ignoring the bracketed phrase, this gives us 8*3!*6*5*4 = 5760 possibilities. To take account of the bracket, we need to exclude cases where there are three Os in a row and three Xs in a row: none of them can be a diagonal, and if a particular row is taken, there are only two other possible rows, so we need to exclude 6*3!*2*3! = 432 cases. So we are looking at 5760-432 = 5328 possibilities for games ending in a win on the sixth move."

Why is the formula so? How did he know what to multiply with?

Answer 1

Yes. How many different possible tic-tac-toe games are there?
It would be an easy calculation if all games lasted 9 moves.
123
456
789
Lets say you picked 1 and I picked 2, then you picked 5 and I picked 3, then you picked 9. You won the game. But the game only lasted 5 moves.
So the calculation has to be broken down into how many moves the games last.
That's what they have done in their calculation.

Answer 2

Hmm...Im confused too....