"In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?" Code Answer's
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In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
By 
Troubled Thrush
on Mar 30, 2021
Troubled Thrush
on Mar 30, 2021
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.0
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