Consider the game of backgammon, in which moves are based on the outcome of rolling a pair of balanced dice. Each roll outcome is an ordered pair. A player may move any one of her pieces a number of points exactly as far (in terms of number of points shown on the board) as the amount shown on one die and then move that piece, or another piece, exactly the number of points shown on the other die. If she rolls doubles, she may make four moves, each move corresponding to the amount shown on one of the dice. .Prepare a table showing the distance (number of points)that a piece can advance following a single roll of two dice. Beside each distance, list the number of roll outcomes that would allow the piece to move that distance.