Latest self Aptitude Question SOLUTION: Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?

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(#M40002352) SELF question chess board Keep an EYE

Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?

virendra (12 years ago)

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Debadrita Datta  (12 years ago)

thr are 8 rows and 8 columns, so 8 squares in each row nd column... so in each row or column, the no. of pairs of adjacent squares will be 8-1=7.
now row wise there will exist 7*8=56 nos of such pairs as there are 8 rows in total and similarly 7*8 nos of such pairs column wise.
so total no. of such cases =7*8+7*8=112
now total no. of pairs is 64C2
so reqd probability = 112/64C2 = 1/18

Is this solution Helpfull? Yes (19) | No (2)  

Ambika Prasad Tiwari  (12 years ago)

there are 4 types of square at corner who have 2 neighbours
there are 24 types of square at edges of the chessboard who have 3 neighbours
there are rest 64-(24+4)=36 squares who have 4 neighbours
so probability=((4/64)*(2/63))+((24/64)*(3/63))+((36/64)*(4/63))=1/18

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virendra  (12 years ago)

Solution of you both are very good..
Thanks debadrita and ambika.

Is this solution Helpfull? Yes (2) | No (1)  

Atul singh  (9 years ago)

Sample space will be total ways of selecting 2 squares out of available 64 square
So sample space =64C2
7 unique adjacent square sets in each row and each column.
i.e. favourable cases will be 7×(8 rows + 8 columns) = 112.
so probability =112/6c2=1/18

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Dhara Patel  (12 years ago)

8c7 * 8c7 = 64

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