2012 UNCO Math Contest II Problems/Problem 2


Four ordinary, six-sided, fair dice are tossed. What is the probability that the sum of the numbers on top is $5$?


The total possibilities when we roll 4 fair 6-sided dice is $6\cdot 6\cdot 6\cdot 6=1296.$ We see that the only possible way for these dice to have a sum of $5$ is to have $3$ dice with ones on it and one dice with a $2$ on it. This can be done in $4$ ways. Thus, the probability is \[\frac{4}{1296}=\boxed{\frac{1}{324}}\] ~SharpApricot123

See Also

2012 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All UNCO Math Contest Problems and Solutions