In how many different ways can the letters of the word 'INDEPENDENCE' be arranged so that the vowels

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15 Aug 2022 Permutation & Combination

In how many different ways can the letters of the word 'INDEPENDENCE' be arranged so that the vowels always come together?

OPtion

1) 8400
2) 33600
3) 22050
4) 67200
5) 2100
6) 25200
7) 12600
8) 16800
9) 14700
10) None of these

Solution

In the word 'INDEPENDENCE' we have 5 vowels IEEEE and 7 consonants NDPNDNC
We treat vowels IEEEE as one group
Thus, we have letter group NDPNDNC (IEEEE).
This has 8 (7+1) letters of which N occurs 3 times, D occurs 2 times and rest are different.
Number of ways arranging these letters = 8!/(3!x2!) = 3360
Now, 5 vowels in which E occurs 4 times and the rest are different, can be arranged in 5!/4! = 5 ways
.'. Required number of ways = ( 3360 x 5) = 16800
Correct Option 8)

Correct Option: 8 Best Solution (3)

G.S.Kantharao   2 years AGO

Number of ways =(5!/4!)*(8!/3!*2!)=16800
My option is 8 👈

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Aarjav jain   2 years AGO

5!/4! for EEEEI
and 8!/3! * 2! for others
so answer is (5!/4!)*(8!/3!*2!) = 16800

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ARINJOY GHOSH   2 years AGO

The number of ways=(5!/4!)*(8!/(3!2!))=16800
Ans Option (8)

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