This exercise will inspire you and open up many possibilities for your rhythm guitar playing. The full lesson is here!
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I believe the answer to the question of how many combinations there are of 8th note strumming patterns is 8! = 40,320.
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8 Factorial (8!) , for those wanting to get Mathies 
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Bjeezus… yeah maybe I won’t do a book with ALL the patterns then 
lol!
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This is all based around the assumption that your strumming pattern is only one measure long. Theoretically there are infinite possibilities if you don’t limit yourself to repeating one measure patterns
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I believe the answer is actually 255. We’re using quarter notes, not eighth notes, but you can either strum or not strum at each position.
D U D U D U D U
2x2x2x2x2x2x2x2 = 256 but you can’t make a beat with absolutely no sound, so 00000000 is not an option.
If you move to sixteenth notes, you have 2^16 -1 = 65,535
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255 is the correct answer. If you want to have some fun and practice random patterns you can use the calcultor function in windows. Switch to the programmer view and select a number > 128 (so you have a down strum on beat 1) and <= 256 then look at the binary conversion. Example 172 = 1010 1100 in binary this would be D_ D_ DU _ _. Strum the strings on the 1’s.
193 = 11 00 00 01 DU _ _ _ _ _ U.
Computer geeks (like me) would understand.
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I found this exercise hilariously frustrating 
Every time I wrote down a pattern, played it and thought “yeah I like that one” I would realize that it was either the Old Faithful pattern D-DU-UD- or the Distraction pattern DU-U-U-UDU. I did that around 4 times before I could actually come up with a pattern that wasn’t one of those.
I guess the past week of judiciously practicing those two patterns with distractions has paid off, that I’m writing and strumming them subconsciously even when I don’t want to
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Justin’s free Strumming Machine is an excellent tool for learning various patterns. 
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