<p>If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is</p>
Step-by-Step Solution
Key Concept: After fixing R at position 1 and E at position 4, count the remaining available letters from MEDITERRANEAN for positions 2 and 3, accounting for letter frequencies and repetitions.
<p><strong>Step 1:</strong> Identify letters in MEDITERRANEAN.</p><p>M-E-D-I-T-E-R-R-A-N-E-A-N</p><p>Letter frequencies: M(1), E(3), D(1), I(1), T(1), R(2), A(2), N(2)</p><p><strong>Step 2:</strong> Fix R at position 1 and E at position 4.</p><p>Remaining letters available: M(1), E(2), D(1), I(1), T(1), R(1), A(2), N(2)</p><p><strong>Step 3:</strong> Fill positions 2 and 3 with 2 letters from the remaining 13 letters (counting multiplicities).</p><p><strong>Step 4:</strong> Consider cases based on whether the two letters chosen are identical or different:</p><p><strong>Case 1:</strong> Both letters the same: E, A, or N can be used (3 ways)</p><p><strong>Case 2:</strong> Both letters different: Choose 2 from remaining distinct letters and arrange.</p><p>Remaining distinct letters: M, E(2), D, I, T, R, A(2), N(2)</p><p>Total pairs where letters are different = P(13,2) - (pairs of identical letters)</p><p>= 13 × 12 - 3 = 156 - 3 = 153</p><p><strong>Step 5:</strong> Total words = 3 + 153 = <strong>156</strong></p><p>∴ Answer: A</p>
Correct Answer: A