JEE MAIN - Mathematics (2023 - 1st February Morning Shift - No. 19)
The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ___________.
Answer
50400
Explanation
Vowels : A,A,A,I,I,O
Consonants : S,S,S,S,N,N,T
$$ \therefore $$ Total number of ways in which vowels come together
$=\frac{8 !}{4 ! 2 !} \times \frac{6 !}{3 ! 2 !}=50400$
Consonants : S,S,S,S,N,N,T
$$ \therefore $$ Total number of ways in which vowels come together
$=\frac{8 !}{4 ! 2 !} \times \frac{6 !}{3 ! 2 !}=50400$
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