In how many ways can we choose two squares from a 8 by 8 chessboard given we cannot choose two squares that are in the same row or column?
There are 64c2 possible ways of selecting 2 squares on board. Subtract 8c2 *16 to subtract the options where there are two in the same row or column. Is this correct?
Almost. The number of possibilities with two in one row or column are a little bit wrong: Fixing one square there are only 15 elements in the corresponding row/column the other one can not take, not 16. Which one did you count twice?