<p>The number of possible outcomes in a throw of \(n\) ordinary dice in which at least one of the dice shows an odd number is</p>
Step-by-Step Solution
Key Concept: Use complementary counting: subtract the cases where ALL dice show even numbers from the total possible outcomes. This avoids complex casework with 'at least one odd'.
<p><strong>Step 1:</strong> Find total possible outcomes when throwing n dice.</p><p>Each die has 6 faces, so total outcomes = 6ⁿ</p><p><strong>Step 2:</strong> Find outcomes where NO die shows an odd number (all dice show even).</p><p>Each die must show {2, 4, 6}, giving 3 choices per die.</p><p>Number of all-even outcomes = 3ⁿ</p><p><strong>Step 3:</strong> Apply complementary counting.</p><p>Outcomes with at least one odd = Total - All even</p><p>= 6ⁿ - 3ⁿ</p><p>∴ Answer: <strong>6ⁿ - 3ⁿ</strong></p>
Correct Answer: C