<p>Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is</p>
Step-by-Step Solution
Key Concept: Since balls of the same color are identical, we only need to count combinations of quantities. For each color, we can select 0 to n balls independently, then subtract 1 to exclude selecting zero balls of all colors.
<p><strong>Step 1:</strong> Recognize that balls of the same color are identical, so we need to count how many of each color to select.</p><p><strong>Step 2:</strong> For white balls: we can select 0, 1, 2, ..., or 10 balls → 11 ways</p><p><strong>Step 3:</strong> For green balls: we can select 0, 1, 2, ..., or 9 balls → 10 ways</p><p><strong>Step 4:</strong> For black balls: we can select 0, 1, 2, ..., or 7 balls → 8 ways</p><p><strong>Step 5:</strong> Total ways to select = 11 × 10 × 8 = 880 ways (including the case of selecting nothing)</p><p><strong>Step 6:</strong> Since we need to select one or more balls, subtract 1: 880 - 1 = 879</p><p>∴ Answer: D (879)</p>
Correct Answer: D