Consider a set of distinct elements, labeled A, B, C, D, and E. You are tasked with generating all possible permutations of these elements, but with a twist: each permutation must satisfy a specific set of conditions. Here are the conditions:

1. The first element must be either A or B.

2. C must appear before D.

3. E cannot be the last element.

Your challenge is to devise an algorithm or approach that generates all valid permutations while adhering to these conditions. Additionally, determine the total number of valid permutations possible for this set of elements.

Note: In your response, provide both the algorithm or approach used to generate the permutations and the final count of valid permutations satisfying the given conditions.