<p>Find the number of ways in which one or more letters can be selected from the letters AAAAA BBBB CCC DD EFG.</p>
Step-by-Step Solution
Key Concept: For selections from objects that are both identical and distinct, use the formula: (a₁ + 1)(a₂ + 1)...(aₙ + 1) × 2^k - 1, where k is the number of distinct objects.
<p><strong>Step 1:</strong> Here, 5 A's are alike, 4 B's are alike, 3 C's are alike, 2 D's are alike and E, F, G are different.</p><p><strong>Step 2:</strong> Total number of combinations = (5 + 1)(4 + 1)(3 + 1)(2 + 1) × 2³ - 1</p><p><strong>Step 3:</strong> = 6 × 5 × 4 × 3 × 8 - 1</p><p><strong>Step 4:</strong> = 2880 - 1 = 2879</p><p>∴ Answer is 2879 (excluding the case when no letter is selected)</p>
Correct Answer: 2879