When a fair six-sided dice is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the  faces that can be seen is divisible by $6$?
$\textbf{(A)}\ 1/3\qquad\textbf{(B)}\ 1/2\qquad\textbf{(C)}\ 2/3\qquad\textbf{(D)}\ 5/6\qquad\textbf{(E)}\ 1$
We have six cases: each different case, every one where a different number cannot be seen. The rolls that omit numbers one through five are all something times six: an example would be where the number you cannot see is one, so the product should be 2 x 3 x 4 x 5 x 6, and so product should be divisible by six. The roll that omits six on the other hand is 1 x 2 x 3 x 4 x 5, which has 2 x 3, also equal to six. We can see that all of them have a factor of 6 and therefore are divisible by six, so the solution should be E, 1.



[2003 AMC 8](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8) ([Problems](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems) • [Answer Key](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Answer_Key) • [Resources](https://artofproblemsolving.comhttp://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=2003))


Preceded by[Problem 11](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_11)

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[1](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_1) • [2](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_2) • [3](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_3) • [4](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_4) • [5](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_5) • [6](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_6) • [7](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_7) • [8](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_8) • [9](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_9) • [10](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_10) • [11](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_11) • 12 • [13](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_13) • [14](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_14) • [15](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_15) • [16](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_16) • [17](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_17) • [18](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_18) • [19](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_19) • [20](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_20) • [21](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_21) • [22](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_22) • [23](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_23) • [24](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_24) • [25](https://artofproblemsolving.com/wiki/index.php/2003_AMC_8_Problems/Problem_25)


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