Q. 84.0( 4 Votes )

Find the number of arrangements of the letters of the word ‘ALGEBRA’ without altering the relative positions of the vowels and the consonants.

Answer :

To find: number of arrangements without changing the relative position


The following table shows where the vowels and consonants can be placed


Consonants can be placed in the blank places



There are 3 spaces for vowels


There are 3 vowels out of which 2 are alike


Vowels can be placed in 3 ways


There are 4 consonants, and they can be placed in = 24 ways


Total number of arrangements = = 72 ways


72 arrangements can be made


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