<p>The number of selections of 4 letters from the letters of the word MISSISSIPPI is ______.</p>
Step-by-Step Solution
Key Concept: Since MISSISSIPPI has repeated letters (M:1, I:4, S:4, P:2), we must count distinct selections by the frequency of each letter type, not treat letters as distinguishable. We need to find non-negative integer solutions to m + i + s + p = 4 with constraints 0≤m≤1, 0≤i≤4, 0≤s≤4, 0≤p≤2.
<p><strong>Step 1:</strong> Identify letter frequencies in MISSISSIPPI: M appears 1 time, I appears 4 times, S appears 4 times, P appears 2 times.</p><p><strong>Step 2:</strong> A selection of 4 letters is determined by how many of each letter type we choose: (m, i, s, p) where m + i + s + p = 4.</p><p><strong>Step 3:</strong> List all valid selections respecting maximum frequencies (m≤1, i≤4, s≤4, p≤2):</p><p>• (1,3,0,0): MIII</p><p>• (1,2,1,0): MIIS</p><p>• (1,2,0,1): MIIP</p><p>• (1,1,2,0): MISS</p><p>• (1,1,1,1): MISP</p><p>• (1,1,0,2): MIPP</p><p>• (1,0,3,0): MSSS</p><p>• (1,0,2,1): MSSP</p><p>• (1,0,1,2): MSPP</p><p>• (1,0,0,3): Not valid (p≤2)</p><p>• (0,4,0,0): IIII</p><p>• (0,3,1,0): IIIS</p><p>• (0,3,0,1): IIIP</p><p>• (0,2,2,0): IISS</p><p>• (0,2,1,1): IISP</p><p>• (0,2,0,2): IIPP</p><p>• (0,1,3,0): ISSS</p><p>• (0,1,2,1): ISSP</p><p>• (0,1,1,2): ISPP</p><p>• (0,0,4,0): SSSS</p><p>• (0,0,3,1): SSSP</p><p>• (0,0,2,2): SSPP</p><p>∴ <strong>Answer: 23</strong></p>
Correct Answer: 23