Counting problems (permutations and combinations etc.)

Hi! Anyone can help me with any/some/all of the following questions:

1. Determine the number of 4-element subsets {a, b, c, d} of {1, 2, 3, 4,..., 20} such that a + b + c + d is divisible by 3.

*Pretty sure for this one I'll need to use some mod, not sure how though*(Wait)

2. There are 10! permutations s0s1...s9 of 0, 1,...,9. How many of them satisfy sk __>__ k-2 for k = 0, 1,...9?

3. Let S = {1, 2, 3, 4, ..., 50}. Find the number of 3-element subsets {a,b,c} of S that satisfy the following: a + b + c is divisible by 3

4. Let P be a 30-sided polygon inscribed in a circle. Find the number of triangles whose vertices are the vertices of P such that any 2 vertices of each triangle are separated by at least 3 other vertices of P.

Thanks!!(Rofl)