Probablity qn

[Mr B]

Two squares are chosen at random on a chessboard . What is the probability that they
have a side in common?
(a) 1/18
(b) 64/4032
(c) 63/64
(d) 1/9

I get 1/36.
Nr=Possible outcomes is 112
Dr=64x63. 112/(64*63)=1/36

Need help!

[knowpraveen]

The number of possible cases in which the selected squares would have a common side are 112. But, what has gone wrong is the sample space you have considered which amounts to 64x63/2. i.e 64C2.

This is because, you select Row 6, Column 5. If there is another selection in which a person selects Row 6  and Column 4 in that order its the same set that he ends up with when he selects it in the reverse order and not two different ones. Therefore the sample space has 2016 elements in it.

Therefore, P = 1/18

Thanks for the question.

[Mr B]

Thanks. Actually the answers are not available for this. Yes 1/18 sounds right.