<p>Out of 10 white, 9 black, and 7 red balls, find the number of ways in which selection of one or more balls can be made (balls of the same color are identical).</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 choose how many balls of each color (0 or more), then subtract 1 for the case where we select zero balls of all colors.
<p><strong>Step 1:</strong> For white balls: We can select 0, 1, 2, ..., or 10 white balls = 11 ways</p><p><strong>Step 2:</strong> For black balls: We can select 0, 1, 2, ..., or 9 black balls = 10 ways</p><p><strong>Step 3:</strong> For red balls: We can select 0, 1, 2, ..., or 7 red balls = 8 ways</p><p><strong>Step 4:</strong> Total selections (including empty set) = 11 × 10 × 8 = 880</p><p><strong>Step 5:</strong> Since we need 'one or more' balls, subtract the case of selecting zero balls from each color: 880 - 1 = 879</p><p>∴ Answer: <strong>879</strong></p>
Correct Answer: 879