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The letters of the word MODESTY are writ...

The letters of the word MODESTY are written in all possible orders and these words (with or without meaning) are listed as in a dictionary then find the rank of the word MODESTY.

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To find the rank of the word "MODESTY" when all its letters are arranged in alphabetical order, we can follow these steps: ### Step 1: Identify the letters and their order The letters in "MODESTY" are: - D - E - M - O - S - T - Y Arranging these letters in alphabetical order gives us: - D, E, M, O, S, T, Y ### Step 2: Calculate the words starting with letters before 'M' 1. **Words starting with D**: - If 'D' is the first letter, the remaining letters are E, M, O, S, T, Y (6 letters). - The number of arrangements = 6! = 720. 2. **Words starting with E**: - If 'E' is the first letter, the remaining letters are D, M, O, S, T, Y (6 letters). - The number of arrangements = 6! = 720. So, total words before 'M' = 720 + 720 = 1440. ### Step 3: Calculate the words starting with 'M' and letters before 'O' 3. **Words starting with MD**: - If 'M' is the first letter and 'D' is the second, the remaining letters are E, O, S, T, Y (5 letters). - The number of arrangements = 5! = 120. 4. **Words starting with ME**: - If 'M' is the first letter and 'E' is the second, the remaining letters are D, O, S, T, Y (5 letters). - The number of arrangements = 5! = 120. So, total words starting with 'M' before 'MO' = 120 + 120 = 240. ### Step 4: Calculate the words starting with 'MO' and letters before 'D' 5. **Words starting with MO**: - The next letter after 'M' and 'O' is 'D', and the remaining letters are E, S, T, Y (4 letters). - The first word in this sequence is "MODESTY" itself. ### Step 5: Calculate the total rank Now, we sum up all the words counted so far: - Words starting with D = 720 - Words starting with E = 720 - Words starting with MD = 120 - Words starting with ME = 120 - Words starting with MO before "MODESTY" = 0 (since "MODESTY" is the first word) Total words before "MODESTY" = 720 + 720 + 120 + 120 + 0 = 1680. Thus, the rank of "MODESTY" = 1680 + 1 = 1681. ### Final Answer The rank of the word "MODESTY" is **1681**. ---
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