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

• 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
  
• 12 years agoHelpfull: Yes(19) No(2)
• 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
• 12 years agoHelpfull: Yes(6) No(1)
• Solution of you both are very good..
  Thanks debadrita and ambika.
• 12 years agoHelpfull: Yes(2) No(1)
• 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
• 9 years agoHelpfull: Yes(2) No(1)
• 8c7 * 8c7 = 64
• 12 years agoHelpfull: Yes(1) No(3)