Finding different arrangments

The letters A, B, C, D, and E are to be arranged in five different boxes, one in each box in the following way. A must be between C and D, B must be next to E, and C cannot be in the first or fifth positions. How many different arrangements of these letters are possible?

How can you compute that it's 4?

Re: Finding different arrangments

CAD can be the last 3 (but only in that order) wtih BE or EB as the first 2

Or DAC can be the first 3 (but only in that order) BE or EB as the last 2 Hence 4 arrangements