Two white pawns are placed at random on the third row of a chessboard. Assume that the chessboard is oriented in such a way that the allowable moves for the pawn are in the fourth row (in other words the bottom right extreme square is white). A black knight is placed at random on the fourth row. Assume that the only other pieces on the board are the two kings and that they occupy the first and last rows.
Compute:the probability that the knight can be captured in the next move, if it is white’s turn;
My Approach:- the pawns can either be placed as:- (a) both not in corners (b) one in corner and the other not in corner (c) both in corners. Which will allow 4,3 and 2 places respectively for the knights to be positioned in order to be eliminated. the answer in that case would be (6/8)(5/7)(4/8)+(6/8)(2/8)(3/8)2+(2/8)(1/7)*(2/8) which is not equal to the answer which is 23/56, How have I erred?