Since all the vowels and consonants have to be together there can only be there are 5! way to order the vowels and 4! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.

So 5!4!2! (D)

Treat vowels like a unit and consonants like a unit --> We know the blocks could be arranged in two ways (1)

(2) Number of ways vowels can be arranged --> 5!

(3) Number of ways consonants can be arranged --> 4!

(1)(2)(3) = 2x5!x4!

D.

We need to determine the number of ways to arrange the letters of word "EDUCATION" such that all the vowels as well as all the consonants always appear together. We start by arranging the given word with vowels together with the consonants together.

[EUAIO] [DCTN]

We first see that there are 2 ways to arrange [EUAIO] and [DCTN]: [EUAIO] [DCTN], [DCTN] [EUAIO].

Next we must determine the number of arrangements for the letters in [EUAIO] and in [DCTN].

[EUAIO] can be arranged in 5! ways.

[DCTN] can be arranged in 4! ways.

Thus, the total number of ways to arrange the letters of word "EDUCATION" such that all the vowels as well as all the consonants always appear together is 5! x 4! x 2, or 5! x 4! x 2!.

Answer: D
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