Question 1062142
Look at cube 1
10
Draw a table
=0==2===4==6====8===10
0
2
4
6
8
10
If the first cube is 10, the second and third must sum to 12 or more.  That is 2 and 10 in second row
4, and 8 or 10 in the third row; 6 and 6,8,10 in the fourth row; 8 and 4,6,8,10 in the fifth row, and 10 and 2,4,6,8,10 in the last row.  There are 15 possibilities out of the 36 combinations or 15/36
Multiply that by 1/6 chance first is 10, and the probability is 15/216.
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Make the first cube 8 with 1/6 probability.
Now the pyramid of choices that work has shifted down so instead of 1,2,3,4,5 that work, it is 1,2,3,4 or 10 possibilities.  The joint probability is 10/216
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Make the first cube 6 with 1/6 probability and the rows that work have 1,2,3 choices or 6/36 probability.  The joint probability is 6/216.
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Make the first cube 4 and there are only 1, 2 choices or 3/36 probability.  That is 3/216 joint probability.
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Make the first cube 2, and there is only one choice, 10 and 10 with 1/36 probability and 1/216 joint probability.
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If the first cube is 0, there is no chance.
The joint probabilities sum to 15+10+6+3+1 , with denominator 216. The answer is 35/216.