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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: How many distinct 7-letter words can be formed from the letters of QUANTUM if the vowels must occupy the first and last positions?

📌 U and U: 1 way (positions 1 and 7), but since U is repeated, the number of distinct arrangements is 1 (U-U) or 1 (U-A), etc. Wait, better approach:

📌 Vowels available: U, A, U. For first and last positions:

📌 Case 1: Both Us. Number of arrangements: 1 (U at 1, U at 7, but since U is identical, only 1 distinct way).

📌 Case 2: First U, last A or first A, last U. There are 2 possibilities: (U, A) or (A, U).

📌 Number of ways to arrange vowels in first and last positions without consecutive repetition:

📌 If both vowels are U: 1 (U at 1, U at 7).

📌 If vowels are U and A (in either order): 2.

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