ELI5 the formula to figure out all possible combinations without repeating any items but no upper or lower limit of the number to include. Order does not matter.
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1What have you tried? Where are you stuck? – rogerl Sep 20 '19 at 01:41
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I don't even know where to start. I am assuming it is a simple formula, but I don't even know where to start. – jtgis Sep 20 '19 at 01:43
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4Hint: in any combination, every ball of the 100 is either in that combination or out of it. – rogerl Sep 20 '19 at 01:44
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1Each item can be in or out, independently. Hence $2^{100}$. – David G. Stork Sep 20 '19 at 01:45
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Is there a formula for this? What is it called? I need the formula to take a list of these and then spit out the lists of all of the combinations. – jtgis Sep 20 '19 at 02:03
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1The list of combinations is far to long to spit out. The computation of how many there are is the multiplication principle. – Ross Millikan Sep 20 '19 at 03:25
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You can pick up $k$ items out of $100$ where $k=0,1,2,\ldots ,100$
Hence, all the possibilities are:
$$\sum_{k=0}^{100} \binom{100}{k}=2^{100}$$
Ng Chung Tak
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