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Trying to figure out how to calculate all possible finger combinations on a piano. Since we have 10 fingers we can play a note with just 1 finger (one note),with all 10 fingers (notes) or with a number of combination of fingers of both hands, and that is what I want to figure out.

However I want to figure out all the possible combinations, for example left hand finger 1,3 with right hand fingers 4,5 etc.

Thank you in advance

budhallah
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    In each combination you can choose to use a certain finger or not, that is, two options per finger. The total number of combinations then must be $2^{10}$. – Marc May 29 '14 at 14:11
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    In practice, one often plays multiple notes with a single finger as well – MPW May 29 '14 at 14:11
  • No problem, don't forget that if you don't want the empty set, ie the combination where all fingers do nothing, you have to subtract one. – Marc May 29 '14 at 16:40

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As Marc points out every combination of fingers corresponds to a subset of the set of fingers: $\{\text{left pinky,left ring finger,left middle finger, } \dots \text{, right pinky}\}$. Therefore the number of combinations of fingers is $2^n-1$ since the empty subset correspods to not doing anything, which is not something that needs to be practiced.

Asinomás
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