$5$ dots on a $8$x$8$ board
Solution 1:
To the numerator you need to multiply by $5!$ for the ways to permute the dots in the chosen five rows and columns, since there must be exactly one in each row and column of the induced submatrix.
To the numerator you need to multiply by $5!$ for the ways to permute the dots in the chosen five rows and columns, since there must be exactly one in each row and column of the induced submatrix.