Question

How many 5-letter words may be formed from BCDEA (with no repetition of letters) so that the consonants are not all separated from each other by vowels.

The answer is supposed to be 108 but I honestly have no idea how to even begin approaching this problem.
Total cases: 5! = 120

Case to eliminate: BECAD

3x2x2x1 = 12

120 - 12 = 108

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