JEE MAIN - Mathematics (2020 - 6th September Evening Slot - No. 13)
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 ________ .
Answer
120
Explanation
Consonants $$ \to $$ LTTR
Vowels $$ \to $$ EE
Total No of words = $${{6!} \over {2!2!}}$$ = 180
Total no of words if vowels are together
= $${{5!} \over {2!}}$$ = 60
$$ \therefore $$ Total no of words where
vowels never come together = 180 – 60 = 120.
Vowels $$ \to $$ EE
Total No of words = $${{6!} \over {2!2!}}$$ = 180
Total no of words if vowels are together
= $${{5!} \over {2!}}$$ = 60
$$ \therefore $$ Total no of words where
vowels never come together = 180 – 60 = 120.
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