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Rolling four standard dice, what is the probability that the product of the four results is even and divisible by 3?

 Sep 5, 2021
 #1
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133 ones   [ 4 dice beginning with 1]
152 twos  [4 dice beginning with 2 ]
189 threes[4 dice beginning with 3]
152 fours  [4 dice beginning with 4]
133 fives  [4 dice beginning with 5 ]
216 sixes [4 dice beginning with 6 ]
Total number of all possible permutations of the products of 4 dice that are all even and divisible by 3== 133 + 152 + 189 + 152 + 133 + 216==975
The probability is: 975 / 6^4==325 / 432

 Sep 5, 2021
 #2
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I decided to verify this with programming and found that my program gave the answer as 974. I didn't include details about distribution with that, but a little more poking around with it revealed that the program only found 188 instances of "threes" to your 189. I don't blame you for getting that wrong, counting is hard

helperid1839321  Sep 6, 2021

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