# How many words can be formed by arranging the letters of the word ‘ARRANGEMENT’, so that the vowels remain together?

To find: number of words where vowels are together

Vowels in the above word are: A,A,E,E

Consonants in the above word: R,R,N,G,M,N,T

Let us denote the all the vowels by a single letter say Z

the word now has the letters, R,R,N,G,M,N,T,Z

R and N are repeated twice

Number of permutations =

Now Z is comprised of 4 letters which can be permuted amongst themselves

A and E are repeated twice

number of permutations of Z =

Total number of permutations =

The number of words that can be formed is 60480

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