<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 the number of ways to select quantities of each color independently. For each color, we can select 0, 1, 2, ... up to the maximum available, then subtract 1 for the case where we select nothing from all colors.
<p><strong>Step 1:</strong> Identify that balls of the same color are identical, so we only care about <em>how many</em> of each color we select, not <em>which specific</em> balls.</p><p><strong>Step 2:</strong> For white balls: we can select 0, 1, 2, ..., or 10 balls → 11 choices</p><p><strong>Step 3:</strong> For green balls: we can select 0, 1, 2, ..., or 9 balls → 10 choices</p><p><strong>Step 4:</strong> For black balls: we can select 0, 1, 2, ..., or 7 balls → 8 choices</p><p><strong>Step 5:</strong> Total selections = 11 × 10 × 8 = 880</p><p><strong>Step 6:</strong> Subtract 1 for the case where we select 0 balls from all colors (since we need 'one or more' balls)</p><p>∴ Answer: 880 - 1 = <strong>879</strong></p>
Correct Answer: D