Three dice thrown simultaneously.
Three fair cubical dice are thrown. If the probability that the product of the scores on the three dice is
is
, where
are positive coprime integers, then find the value of
.
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The answer is 35.
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1 solution
A product of 9 0 can only be obtained if the dice show values of 6 , 5 and 3 . Considering the dice as distinct, there are 3 ! = 6 ways this result can be obtained, out of a total of 6 3 outcomes. Thus the desired probability is
6 3 6 = 3 6 1 , and thus b − a = 3 6 − 1 = 3 5 .