The number of arrangements which can be made out of the letters of the word ALGEBRA, without changing the relative order(positions) of vowels and consonents.

here three vowels have to be placed at 1st , 4th and 7th position and the consonants are to be placed at other remaining positions .

 

So , number of arangements = fact(3)/fact(2)  * fact(4) = 72   { fact(2) is becose of 2 A's }