If three squares are chosen at random on a chess board. Show that the chances that they should be in a diagonal line is 7/744
There will be 4 diagonals line comprising 3,4,5,6,7 chess squares and 2 diagonals of 8 chess squares so by selecting any one diagonals and selecting any of the three chess boxes will do our work...
So,
[ 4×{3¢3+4¢3+5¢3+6¢3+7¢3} +2{8¢3} ]/64¢3
=7/744