Three squares chosen at random on the chess board

Question

Three squares are chosen at random on the chess board. The chance that they are in diagonal line is

I found favorable outcomes are $4* \left( {3\choose3} + {4\choose3} + {5\choose 3} + {6\choose3} + {7\choose3} \right)$ and the total number of ways are $64\choose3 $ this gives the answer $\frac{5}{ 744}$ but the correct answer is $\frac{7}{744}$ what event am I missing, thanks.

Answer 1

I think you're missing a summand of $2 * \binom{8}{3}$ in your numerator, accounting for the main diagonals a1-h8 and a8-h1.