5. Tic-Tac-Toe (from 6th grade, 1 point). A tic-tac-toe board (three by three cells) is randomly filled with six X's and three O's. Find the probability that all three O's will end up in a "winning position," that is, in a row either vertically, horizontally, or diagonally.
Solution. The total number of ways to randomly place three noughts and six crosses is $C_{9}^{3}=84$. The number of winning positions for noughts is eight: three verticals, three horizontals, and two diagonals. Therefore, the desired probability is $\frac{8}{84}=\frac{2}{21}$.

Answer: $\frac{2}{21}$.