COMC 2014 B Problem 3

5~ \mathrm{Xs} and 4~ \mathrm{Os} are arranged in the below grid such that each number is covered by either an \mathrm{X} or an \mathrm{O}. There are a total of 126 different ways that the \mathrm{Xs} and \mathrm{Os} can be placed. Of these 126 ways, how many of them contain a line of 3 Os and no line of 3~ \mathrm{Xs}?

A line of 3 in a row can be a horizontal line, a vertical line, or one of the diagonal lines 1-5-9 or 7-5-3.

\begin{array}{|c|c|c| } \hline 1 &2 & 3 \\ \hline 4 & 5 & 6 \\ \hline 7 & 8 & 9 \\ \hline \end{array}