1. Four (standard) dice (cubes with 1,2,3,4,5,6 respectively,dots on their six faces) each of a different color are tossed each landing with one of its faces up, thereby showing a number of dots. Determine the following probabilities.

a. the probability that the total number of dots shown is 6
b. the probability that at most two of the dice show exactly one dot
c. the probability that each die shows at least two dots
d. the probability that the four numbers of dots shown are all different
e. the probability that there are exactly two different numbers of dots shown

Solution Preview

Four dice are tossed and there are 6^4 = 1296 permutations.
a. If the total number of dots is 6, then the possible combinations are (1,1,1,3) and (1,1,2,2), each has 4! = 24
permutations. Thus the probability is (24 + 24) / 1296 = 1/27
b. If at most two of dice show ...

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