### probability - Three squares of a chess board being ...

The number of ways to choose two black and one white square is ${32 choose 2}32$ with the first factor from choosing the two black squares and the second from choosing the white square. Two white and one black is the same by symmetry. There are ${64 choose 3}$ ways to choose three squares, so the chance you want is $$frac {2cdot {32 choose 2}cdot 32}{{64 choose 3}}=frac {16}{21 ...