Given letters A,L,G,E,B,R,A=7 letters.
Vowels =A,E,A
Consonants =L,G,B,R
Total permutations of the letters =7!2!
Permutations of vowels =3!2!=3
Permutations of consonants =4!=24.
Out of 3 ways only one has the order A,E,A ξ similarly out of 24 only 1 has the order L,G,B,R.
∴ By symmitry total possibilities of word with order of vowels ξ consonants fixed is 13×124×7!2!
Required =35.
Hence, the answer is 35.