# How many ways are there to arrange the letters of word $ALGEBRA$ such that the relative order of the vowels and consonants doesn't change?

I did this question this way :-

there are 4 consonants in the words (LGBR) and there are 7 letters in the word.

$therefore$ number of in which consonants can be arranged in relative order will be $C(7,4)$ and there will be 1 arrangement of vowels for each $C(7,4)$ choices.

$C(7,4) * 1$ = $\frac{7!}{4!(7-4)!}$ = $\frac{7!}{4!3!}$ = $35$