<p>Number of ways of selecting one or more balls from 10 white, 9 green, and 7 black balls is:</p>
Step-by-Step Solution
Key Concept: Each color group is independent; for each color, we can select 0 to n balls, giving (n+1) choices. Multiply across colors, then subtract 1 to exclude selecting zero balls from all colors.
<p><strong>Step 1:</strong> Recognize that balls of the same color are identical, so we only count how many of each color to select.</p><p><strong>Step 2:</strong> For 10 white balls: we can select 0, 1, 2, ..., or 10 balls → <strong>11 ways</strong></p><p><strong>Step 3:</strong> For 9 green balls: we can select 0, 1, 2, ..., or 9 balls → <strong>10 ways</strong></p><p><strong>Step 4:</strong> For 7 black balls: we can select 0, 1, 2, ..., or 7 balls → <strong>8 ways</strong></p><p><strong>Step 5:</strong> Total selections = 11 × 10 × 8 = <strong>880</strong></p><p><strong>Step 6:</strong> Subtract 1 for the case where we select 0 balls from each color (null selection): 880 − 1 = <strong>879</strong></p><p>∴ Answer: <strong>D (879)</strong></p>
Correct Answer: D