# Same Diagonal

Question: 3 blocks are chosen randomly on a chessboard. What is the probability that they are in the same diagonal?

There are total of 64 blocks on a chessboard. So 3 blocks can be chosen out of 64 in 64C3 ways.

So the sample space is = 41664

There are 2 diagonal on chessboard each one having 8 blocks. Consider one of them.

3 blocks out of 8 blocks in diagonal can be chosen in 8C3 ways.

But there are 2 such diagonals, hence favourables = 2 * 8C3 = 2 * 56 = 112

The require probability is

= 112 / 41664

= 1 / 372

= 0.002688