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Question

Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements do all vowels occur together.

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Solution

INDEPENDENCE
Arranging 5 vowels
Since vowels are coming together
they can be EEEEI,IEEEE, and So on
In IEEEE there are 4E
since letter are repeating total arrangement =5!4!
Arranging Remaining
no we need to arrange
7+1=8
Hence are 3N,2D
We use=8!3!2!
Required No. =5!4!×8!3!2!
=(8×7×6×5×4)(5×4!)4!×3!×2
=16,800

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