Number of Combinations Created from Restricting a Set
Here?s my question:
I have a set that looks like this:
S = {u, v , w , x , y , z}
And it has this restriction:
1 =< u < v < w < x < y < z <= 11
Essentially, of 6 values, all of them must be greater than or equal to 1, must be less than their successor, must be greater than their predecessor, and must be less than or equal to 11.
How many sets produced from this restriction?
Thank you in advance.
Answer
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Great answer and really intuitive. If you were interested, this is actually a question in disguise that is analyzing the number of scales that can be formed with 7 notes. Thank you so much :)

Interesting! I am glad I was able to help.
The answer is accepted.
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