what is the probability that a rectangle selected at random from a 8*8 chess board is a square?

1) 0
2) 17/108
3) 64/1296
4) 1

• Total no. Of squares are :-
  Square of size 1X1= 64=8^2 .
  2X2 =49= 7^2
  And so on. 8X8=1=. 1^2
  
  So total squares using n(n+1)(2n+1)/6 where n=8
  
  Total rectangles : we need to choose 2 out of 9 lines across ech dimension to make it a square, that is, 9c 2 .
  
  So ans is ( 8*9*17/6 )/ 9c2 * 9c2 equals 17/108
  
• 11 years agoHelpfull: Yes(1) No(2)