Three dice totalling ten

Question

Three fair six-sided dice are thrown. What is the chance their faces add up to exactly $10$ ?

Short answer

$\tfrac18$ . The unordered triples summing to 10 are $\{1,3,6\},\{1,4,5\},\{2,3,5\}$ (six orderings each) and $\{2,2,6\},\{2,4,4\},\{3,3,4\}$ (three orderings each), giving $18+9=27$ outcomes out of $216$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Counting and Combinatorics
Expectation, Mean, and Variance
Series and the Geometric Series: Partial Sums and Convergence

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