Three dice are thrown. What is the probability of getting a sum which is a perfect square?

Explanation

The possible sums for three dice range from 3 to 18. The perfect squares in this range are 4, 9, 16. Number of ways to get a sum of 4: (1,1,2) with permutations = 3. Sum of 9: partitions (1,2,6), (1,3,5), (2,3,4) have 6 permutations each; (1,4,4), (2,2,5) have 3 permutations each; (3,3,3) has 1. Total ways for 9 = 18 + 6 + 1 = 25. Sum of 16: (4,6,6), (5,5,6) have 3 permutations each, total 6. Total favorable outcomes = 3 + 25 + 6 = 34. Total possible outcomes = 6^3 = 216. Probability = \frac{34}{216} = \frac{17}{108}.

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