At first sight it could be simplified to:
```
[option not in [None, False] for option in mutually_exclusive_options].count(True)
```
But I have a feeling even more simplification might be possible.

Note that we can't simply cast default to bool, which would make this even simpler, as some valid dates evaluate to false: https://mail.python.org/pipermail/python-ideas/2014-March/026446.html