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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.

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

Is my answer correct ?

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If I understand well, you have to keep the consonants in the same order as in the original word, and the same for vowels.

For example, LGBRAEA would be acceptable, but not AGLEBRA

In that case, your answer is correct.

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