Random number generator with custom settings

Random Number Generator with Custom Settings

Need the ability to choose range of numbers to generate from.
Number of numbers to generate.
Exceptions: Which numbers from range to omit from generation.
Exceptions 2: Which combinations to exclude.
Exceptions 3: If (x) which combinations to exclude.
Must use: Number or numbers that must be generated.

As an example.

Need 5 numbers from 1-20.
Exclude "2,10,11,14,19".
Exclude these combinations, this list must be able to handle thousands of combinations.
1,3,6
1,3,9
1,3,13
1,6,9
1,6,13
1,9,13
3,6,9
3,6,13
3,9,13
6,9,13
etc...

Exceptions 3:

If (15) exclude these combinations
6,12
6,18
6,20
12,18
12,20
18,20

If (12) exclude these combinations
4,9
4,16
4,17
9,16
9,17
16,17

Must use numbers (12,15)

Results should look something like this.

3,8,12,13,15


If the number generator cant generate a number without breaking any of the rules, then it must display an error and not generate a number.

Let me know if you have questions.

Matlab or Excel Macros only.