Correct : a

Explanation:
1. Identify Single-Trial Probabilities:
• Probability of rolling a '6' on a single roll, p = 1/6
• Probability of not rolling a '6' on a single roll, q = 1 - 1/6 = 5/6

2. Determine the Structure of the Target Outcome:
We are looking for the probability of getting exactly one '6' in three rolls. This specific outcome can happen in three different arrangements:
• Arrangement 1: ('6', 'Not 6', 'Not 6') → Probability = (1/6) × (5/6) × (5/6) = 25/216
• Arrangement 2: ('Not 6', '6', 'Not 6') → Probability = (5/6) × (1/6) × (5/6) = 25/216
• Arrangement 3: ('Not 6', 'Not 6', '6') → Probability = (5/6) × (5/6) × (1/6) = 25/216

3. Alternative Binomial Method:
Using the Binomial Probability formula, P(X = k) = ⁿC_k × p^k × q^{n - k}, where:
• n = 3 (number of trials)
• k = 1 (number of desired successes)
    P(X = 1) = ³C₁ × (1/6)¹ × (5/6)²
    P(X = 1) = 3 × (1/6) × (25/36)
    P(X = 1) = 3 × (25/216) = 75/216

4. Conclusion: The total probability of rolling '6' exactly once is 75/216.