3 blocks

Puzzle Question:

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

Answer --

Solution of Puzzle:

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

Toughness:

Intermediate