Q. Two small squares on a chess board are chosen at random. Find the probability that they have a common side

option
A)1/12
B)1/18
C)2/15
D)3/14

• there are total 64 squares. 36 of them have common edges with 4 squares. these 36 squares are located at the center. the 4 corner squares have 2 squares with common edges. the remaining 24 boundary squares have 3 squares with common edges. now 2 squares are to be selected. so out of 36 centre squares 1 can be selected in 36c1 ways and the common edge square can be selected in 4c1 ways or 1 square from 24 boundary squares can be selected in 24c1 waays and the common edge square can be selected in 3c1 ways or 1 square from the 4 corner squares can e selected in 4c1 ways and the common edge sqaure can be selected in 2c1 ways. so total ways are 36c1*4c1+24c1*3c1+4c1*2c1. hence the probability is = (36c1*4c1+24c1*3c1+4c1*2c1)/64c2 = 1/18
• 11 years agoHelpfull: Yes(2) No(2)
• 1/18....for corners..8/63*64
  for sqrs with 3 sides common to oyhr sqrs...72/63*64
  for remng sqrs...144/64*63
  add all to get ans
• 11 years agoHelpfull: Yes(1) No(0)
• Answer is 1/18
• 11 years agoHelpfull: Yes(0) No(0)
• can anyone give the proper solution with proper reason. i am getting 1/9 as the answer.
• 11 years agoHelpfull: Yes(0) No(0)