Question

Find the number of arrangements of the letters of the word independence if all vowels come together

Answer 1

There are 5 vowels in INDEPENDENCE
4E & 1I
arranging these vowels first ...to make them come together...
we use.
n!/p1!×p2!×p3! as there are repeating E
so, we get total no. of arrangements = 5!/4! as p1=4 and n=5.

Now,
arranging the remaining letters ,
no. we have 7+1=8

here we have 3N &2D as repeating
so, using the above formula we get
no. of arrangements= 8!/3!×2!
as, p1=3 and p2=2 and n=8 here.

Hence the required no. of arrangements
=5!/4! × 8! / 3!×2!
=16800 ans.
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