Question: Random sick days

I thought I would generate a fun problem for Maple, and see what coding we could come up with.

You happen to be at work one day and overhear the managers talking about taking sick days away from the employees because everyone is taking their sick time around weekends.  The managers have decided to take one more years worth of data before making their decision. 

So you've decided to build a program in Maple for all the employees to use so that when managers look at the data, they will decide not to take sick days away.


So, let's say we have 5 sick days, they will occur Mon - Fri except when there's a holiday in which case one working day on either side of the holiday must be worked and not be taken as a sick day.  We want Maple to give us 5 dates at random.

Additional fun:
Some additional factors to consider :

We also take two weeks holiday during the summer and the company closes for 1 week for Christmas, we wouldn't want Maple to give our sick days falling in those times. 

Supposing also, the employees never get sick and so in that case they need a higher distribution of sick time around the flu season.  Or, supposing they love the summer or winter and would like a higher distribution of sick time during those seasons. 

Another added factor, we don't want to be sick 1 week on either side of our vacation times ... alternatively we would like a higher probability to have a Friday or Monday sick day on either side of our vacation time. 

I've only just dreamed up this problem, kind of fun since we could all use it as a real world application.   Let's see what we can come up with.