In a bag, there are two 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?	Choose the correct choice
A) 60
B) 50
C) 42
D) 84
E) 61
As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:   1) The minimum number on any given die is 1   2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.   With 4 dice, we could end up with any SUM between:   4 (if we rolled 1s on all 4 dice)   to   64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).   Thus, there are only 61 possible sums.   61
<result>E</result>
In a bag, there are two 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?