in a bag , there are two 6 - sided dice ( numbered 1 to 6 ) , 3 12 - sided dice ( numbered 1 to 12 ) , and two 20 - sided dice ( numbered 1 to 20 ) . if 4 of these dice are selected at random from the bag , and then the 4 are rolled and we find the sum of numbers showing on the 4 dice , how many different possible totals are there for this sum ?