<p>The number of selections of 6 different letters that can be made from the words SUMAN and DIVYA so that each selection contains 3 letters from each word is ___.</p>
Step-by-Step Solution
Key Concept: Since SUMAN and DIVYA each contain 5 distinct letters, we need to select 3 letters from SUMAN's 5 letters AND 3 letters from DIVYA's 5 letters independently, then multiply these counts.
<p><strong>Step 1:</strong> Identify the letters in each word.</p><p>SUMAN has 5 distinct letters: S, U, M, A, N</p><p>DIVYA has 5 distinct letters: D, I, V, Y, A</p><p><strong>Step 2:</strong> Apply the multiplication principle for independent selections.</p><p>• Ways to select 3 letters from SUMAN = C(5,3) = 10</p><p>• Ways to select 3 letters from DIVYA = C(5,3) = 10</p><p><strong>Step 3:</strong> Calculate total selections.</p><p>Since we need 3 from each word and the selections are independent:</p><p>Total selections = C(5,3) × C(5,3) = 10 × 10 = 100</p><p>∴ Answer: <strong>100</strong></p>
Correct Answer: 100