Calculating Permutations With Several Rules

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Apr 20, 2019
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So, I'm in high school, and at the beginning of every Fall Semester, we get a new schedule, which consists of 8 blocks (periods). So a friend & I were curious of the probability to get a certain amount of classes together.

Before trying to calculate, I need to explain what I dubbed, anchor classes. An "anchor class" is a class that is only offered only at a certain block. This block cannot be moved to a different block. With the anchor classes, our 4th block is set together

So if I write out our classes with the anchor classes in mind:
My ClassesMy Friends Classes
1.1.
2. Jazz Band2.
3. 3.
4. AP Music Theory4. AP Music Theory
5.5. Musical Theatre
6. AP Chemistry6. Chamber Choir
7. Band7.
8.8.

The core classes we can possibly have together next year are: English, Government and Economics
These classes can be situated anywhere on the schedule. If for instance my first block is Government and hers is English, that wouldn't count as having a class together. But if we both have English 1st Block, that would count as having a class together. Basically, if the classes match horizontally on the chart, it counts as having a class together. If not, it doesn't.

I'm also being a TA next year, so I can TA for any block of my choosing. So if I TA for the block she is in, that counts as having a block together

Unfortunately, there are two blocks I have no knowledge of that she enrolled in next year. But it is certain that those two blocks are not any of the classes I enrolled in. We'll call these two class both X.

Now there are rules for the TA blocking:
1. I cannot TA for her 5th block class (Musical Theatre)
2. It is assumed that I cannot TA for both X classes
3. The only classes I can TA for are the Core Classes

Not counting AP Music Theory, it seems there are 3 classes I could have her in. I understand permutations would be needed to get the amount of possibilities of having a class together. But I don't know how to calculate it with all these rules. Any help would be most appreciated!

yeah we are both music nerds, everyones got their thing ;)
 
What have you tried? Where are you stuck? Please give us something so that we can help you.
 
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