In how many ways can the letters of the word ALGEBRA be arranged without changing the relative order of the vowels and consonants?

Explanation

There are `4` consonants in the word 'ALGEBRA'.


The consonants are L, G, B, R. they `4` letters.

So, the number of ways to arrange these consonants = `4!`

There are `3` vowels in the given word of which `2` are A'S
The vowels can be arranged among themselves in `3!2! `ways.

Hence, the required number of arrangements

=`4!×3!2`

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