In how many ways can the letters of the word 'ALGEBRA'

The relative positions of all the vowels and consonants is fixed.

The first letter is a vowel. It can be selected out of the 3 three vowels, of which two are same. So, the vowels can be arranged in selecting 3 things, of which two are of the same kind

$\Rightarrow \frac{3 !}{2 !}$

The second, third, fifth and sixth letters are consonants that can be filled by the available 4 consonants in 4! ways.

$\therefore$ By fundamental principle of counting, the number of words that can be formed $=4 ! \times \frac{3 !}{2 !}=72$