Three dice are thrown simultaneously. Find the probability that: (i)all of them show the same face. (ii)all show distinct faces. (iii)two of them show the same face.

Explanation

To solve the problem of finding the probabilities for the three scenarios when three dice are thrown simultaneously, we will follow a systematic approach.

### Total Outcomes
When three dice are thrown, each die has 6 faces. Therefore, the total number of possible outcomes when throwing three dice is:
\[ N(S) = 6 \times 6 \times 6 = 6^3 = 216 \]

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