N2009 P2 Q8

Find the number of ways in which the letters of the word ELEVATED can be arranged if

1. there are no restrictions,[1]
2. T and D must not be next to one another,[2]
3. consonants (L, V, T, D) and vowels (E, A) must alternate,[3]
4. between any two Es there must be at least \(2\) other letters.[3]