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 __________ . [2023]

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Solution

Q.
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 __________ . [2023]

Ans.
(50400)

In the word ASSASSINATION, there are 6 vowels A A A I I O and consonants S S S S N N T.

$Taking (AAAIIO) as a single unit, we get:$

$Number of ways to arrange ASSASSINATION such that all vowels occur together$

$= \frac{8!}{4! 2!} \times \frac{6!}{3! 2!} = \frac{8! \times 6!}{4! {(2!)}^{2} 3!} = 50, 400$

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