Take the task of arranging the letters and break it into stages.
DESIGN has 6 letters. So, we must place each letter in one of six spaces.

We’ll begin with the most restrictive stage.

Stage 1: Select a letter for space #1
Since this letter must be either E or I, we can complete stage 1 in 2 ways

Stage 2: Select a letter for space #6
This letter must also be a vowel. Since we already placed one of the two vowels in space #1, the remaining vowel must be placed in space #6.
So, we can complete stage 2 in 1 way

Stage 3: Select a letter for space #2
There are 4 letters remaining to be placed, so we can complete stage 3 in 4 ways

Stage 4: Select a letter for space #3
There are 3 letters remaining, so we can complete stage 4 in 3 ways

Stage 5: Select a letter for space #4
There are 2 letters remaining, so we can complete stage 5 in 2 ways

Stage 6: Select a letter for space #5
There is 1 letter remaining, so we can complete stage 6 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus arrange all 6 letters) in (2)(1)(4)(3)(2)(1) ways (= 48 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.

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