Let $$U = \{ 1,2,....,n\} $$, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with $$|A| = |B| = k$$ and $$A \cap B = \phi $$. We say that a permutation of U separates A from B if one of the following is true.
- All members of A appear in the permutation before any of the members of B.
- All members of B appear in the permutation before any of the members of A.
How many permutations of U separate A from B?
There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:
- The fastest computer gets the toughest job and the slowest computer gets the easiest job.
- Every computer gets at least one job.
The number of ways in which this can be done is ______