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Is there a formula or perhaps an automatic calculator online (or a method in excel) by which I can calculate the total number of combinations one can pick of all sizes from a set of n items?

i.e. if n = 4, I would like the quantity of values from r=1 to r=4 (which works out to 15, but I need a formula or computational method to do it automatically for any value of n.

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    Do you mean $\sum_{i=0}^n \binom ni$? That's just $2^n$. (if you want the sum to start at $i=1$ it's $2^n-1$, as in $2^4-1=15$). This follows from the binomial theorem (or from counting the subsets of $\{1,\cdots, n\}$) – 2017-01-04
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    How did I not think of that....so elegant and straightforward. Put it into an answer if you wish so I can mark as best. – 2017-01-04

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