The number of words (with or without meaning) that can be formed from all the letters of the word "L

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

Professor PC Thomas Classes · Answer

(120) : There are 2 vowels E, E and 4 consonants L, T, T, R in the word LETTER.\ Total number of possible words that can be formed from all the letters of the word LETTER $=\frac{6!}{2!2!}=180$\ Now, if we consider the vowels EE as single letter, then number of possible words $=\frac{5!}{2!}=60$\ Now, required number of words\ $=$ Total number of words - number of words in which vowels come together\ $=180-60=120$\