Question

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers on the top faces is ?

• A. \(\tfrac{1}{9}\)
• B. \(\tfrac{7}{72}\)
• C. \(\tfrac{5}{36}\)
• D. \(\tfrac{1}{8}\)

Hint:

For sum of 3 dice, either list systematically or recall standard distribution for 3 dice sums.
- \(\sum=10\) has 27 outcomes among 216 total.

Answer 1

The Correct Option is D

Step 1: Count favorable outcomes for sum = 10.
Possible outcomes when rolling 3 fair six-sided dice: total is \(6^3=216\). For a sum of 10, we can systematically list or use combinatorial reasoning. The distinct triples \((x,y,z)\) (with \(1\le x,y,z\le6\)) summing to 10 are: \[ (1,3,6),\;(1,4,5),\;(2,2,6),\;(2,3,5),\;(2,4,4),\;(3,3,4),\;\dots \] Careful enumeration reveals exactly 27 combinations. Step 2: Probability.
Hence \[ P(\text{sum}=10) = \frac{27}{216} = \frac{1}{8}. \]