Q. 65.0( 3 Votes )
How many words can be formed by arranging the letters of the word ‘ARRANGEMENT’, so that the vowels remain together?
Answer :
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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