Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?  Choices:
A) 1/18  B) 64/4032  C) 63/64  D) 1/9  E) 1/4
Explanation :   No of ways of selecting two squares from 64 squares on the chess board is 64C2.   Three cases arise:   case 1: when first square is any of the four corner ones   In this case second square can be chosen in 2 ways   no of ways of selecting two squares: 4*2= 
<gadget id="calculator">4*2</gadget>
<output>8</output>
8   case2: when first square is any of the 24 squares on the side of the chess board other than the corner ones   the second square can be chosen in 3 ways   no of ways of selecting two squares: 24*3= 
<gadget id="calculator">24*3</gadget>
<output>72</output>
72   case 3: the first square is any of the 36 remaining squares   the second square can be chosen in 4 ways   no of ways of selecting two squares: 36*4= 
<gadget id="calculator">36*4</gadget>
<output>144</output>
144   Total no of ways of selecting two adjacent squares= 8 + 72 + 144= 
<gadget id="calculator">8 + 72 + 144</gadget>
<output>224</output>
224   So required probability= 224/64C2 = 224/4032 = 1/18   1/18nswer : 1/18
<result>A</result>
Two squares are chosen at random on a chessboard. What is the probability that they have a side in common?