in how many ways can the letters of the word ALGEBRA be arranged without changing the relative order of the vowels and consonants?

In the word ALGEBRA, there are three vowels (A, A and E) and four consonants (L, G, B and R)

We need to find different arrangements of the word ALGEBRA such that relative positions of vowels and consonants do not change.

Therefore, in the three positions occupied by vowels, we can rearrange the vowels in 3!/2! = 3 ways.

Four consonants can be rearranged in four spaces occupied by consonants in 4! ways = 24 ways.

Therefore, required number of arrangements = 3 x 24 = 72.

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