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As there are 3 dice, it is quite easy (and quick) to work out the possible ways a sum of 10 can be made:

If the first die is a 1, the second and third dice could be {3, 6}; {4, 5}; {5, 4}; {6, 3} - 4 possibilities

If the first die is a 2, the second and third dice could be {2, 6}; {3, 5}; ...; {6, 2} - 5 possibilities

If the first die is a 3, the second and third dice could be {1, 6}; {2, 5}; ...; {6, 1} - 6 possibilities

If the first die is a 4, the second and third dice could be {1, 5}; {2, 4}; ...; {5, 1} - 5 possibilities

If the first die is a 5, the second and third dice could be {1, 4}; {2, 3}; ...; {4, 1} - 4 possibilities

If the first die is a 6, the second and third dice could be {1, 3}; {2, 2}; {3, 1} - 3 possibilities

So there are 4 + 5 + 6 + 5 + 4 + 3 = 27 possible ways of getting a sum of 10

With 3 dice there are 6 × 6 × 6 = 216 possible ways of them landing

→ pr(sum 10) = 27/216 = 1/8 = 0.125 = 12.5%

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It is 0.125

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Q: When three dice are thrown together what is the probability of getting a total score of 10?
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