Three fair dice are rolled simultaneously. What is the probability that the sum of the numbers on the three dice is exactly 10?

hard 5 marks Class 9 · Mathematics · Statistics

Answer

1/8

The correct answer is 1/8 — For each first die value $a$ from 1 to 6, count ordered pairs $(b, c)$ such that $b + c = 10 - a$ within 1–6: - $a = 1$ : 4 pairs - $a = 2$ : 5 pairs - $a = 3$ : 6 pairs - $a = 4$ : 5 pairs - $a = 5$ : 4 pairs - $a = 6$ : 3 pairs

Step-by-step solution

Total outcomes for 3 dice: $6^{3} = 216$ .
For each first die value $a$ from 1 to 6, count ordered pairs $(b, c)$ such that $b + c = 10 - a$ within 1–6: - $a = 1$ : 4 pairs - $a = 2$ : 5 pairs - $a = 3$ : 6 pairs - $a = 4$ : 5 pairs - $a = 5$ : 4 pairs - $a = 6$ : 3 pairs

Common mistake: Missing some ordered triples or counting unordered combinations

Concept tested: Probability of sum of dice

Published 13 October 2026 · How this solution was prepared and checked

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