Question:
The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ________ .
The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is ________ .
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Total arrangements minus arrangements in which the two E's are together.
Updated On: Nov 5, 2026
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Correct Answer: 120
Solution and Explanation
LETTER has 6 letters: L, E, T, T, E, R, with E repeated twice and T repeated twice. Vowels: E, E.
Total words \(= \frac{6!}{2!\,2!} = \frac{720}{4} = 180\).
Words with both E's together: treat EE as one block, giving the 5 objects (EE), L, T, T, R, so the number is \(\frac{5!}{2!} = 60\).
Words in which vowels never come together \(= 180 - 60 = 120\).
Answer: 120
Total words \(= \frac{6!}{2!\,2!} = \frac{720}{4} = 180\).
Words with both E's together: treat EE as one block, giving the 5 objects (EE), L, T, T, R, so the number is \(\frac{5!}{2!} = 60\).
Words in which vowels never come together \(= 180 - 60 = 120\).
Answer: 120
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