Question

In how many ways is it possible to choose two black squares on a 8 X 8 chessboard so that the squares do not lie in the same row or same column?
a. 400
b. 200
c. 800
d. 100
e. 475

Answer 1

First black square:
The total number of squares = 8*8 = 64.
Half are black, half are white.
Number of options for the first black square = 64/2 = 32. The figure above illustrates the number of options for the second black square.
If the first black square selected is the square highlighted in blue, then none of the squares highlighted in red may be chosen as the second black square.
Remaining options for the second black square = 32 - (1 blue square) - (6 red squares) = 25.

To combine the options above, we multiply:
32*25.
Since the order of the two squares doesn't matter, we divide by the number of ways the two squares can be ARRANGED (2!):
(32*25)/(2*1) = 400.