I'm trying to figure out the probability of X or O winning or tie so each turn I want to figure out how many possibilities are that will lead to a win from turn 5-9 which is the only time someone can win because you need 3 to win I was given all the math and answers but I have no idea how they go them so if someone can tell want each number they gave me means it would be greatly appreciated because there's nothing online about it I get the basic math but I just want to know where they got the multiplying numbers from ill put everything I was given below

8*3!*6*5 = 1440 possibilities for games ending in a win on the fifth move.

8*3!*6*5*4 = 5760 possibilities - 6*3!*2*3! = 432 cases = 5328 possibilities for games ending in a win on the 6th move

8*3*6*3!*5*4*3 = 51840 possibilities - 6*3*6*3!*3! = 3888 cases = 47952 possibilities for games ending in a win on the seventh move.

8*3*6*3!*5*4*3*2 = 103680 possibilities - 6*3*6*3!*2*4! = 31104 cases = 72576 possibilities for games ending in a win on the eighth move.

2*3*8*4!*4! = 27648 possibilities + 6*3*4*4!*4! = 41472 possibilities + 22*1*4!*4! = 12672 possibilities = 81792 possibilities for games ending in a win on the ninth move.

6*5!*4! = 46080 possibilities for games ending in a draw on the ninth move.

Win in 5 (X) 1440 0.6% Win in 6 (O) 5328 2.1% Win in 7 (X) 47952 18.8% Win in 8 (0) 72576 28.4% Win in 9 (X) 81792 32.1% Draw 46080 18% total 255, 168 100.0%