If we do not put restrictions on the arrangements of the consonants, then by Formula 4 the number of words that can be formed from the word ALGEBRA is 7!/2!.

If we constrain that the positions of consonants is reserved only for consonants, then the format of the new arrangement should look like this
A, L, G, E, B, R, A
V, C, C, V, C, C, V
V for vowels, C for consonants.

The 4 slots for consonants can be filled in 4P4 = 4! ways, and the 3 slots for vowels can be filled in 3!/2! (A repeats) ways. Hence, by Formula 2, the total number of arrangements in the format is 4!(3!/2!)

\(\frac{4 (\frac{3!}{2!})}{\frac{7!}{2!}}= \frac{1}{35}\)

E is the answer