Question:

Find the number of words which can be formed by using the letters of the word EQUATION if each word has to start with a vowel.

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When a word must “start with a vowel,” first count vowels, then multiply by arrangements of remaining letters.
Updated On: Sep 30, 2025
  • 40320
  • 1260
  • 1080
  • 400
  • 25200
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The Correct Option is

Solution and Explanation

Step 1: Identify vowels.
The word “EQUATION” has 8 distinct letters. Vowels = E, U, A, I, O (5 vowels).

Step 2: Fix the first letter as a vowel.
Choices for first letter = 5.

Step 3: Arrange the remaining 7 letters.
Remaining 7 letters can be arranged in \(7!\) ways.

Step 4: Multiply.
Total words \(= 5 \times 7! = 5 \times 5040 = 25200\).

Final Answer:
\[ \boxed{25200} \]
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