Question 1194127
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Rule: If a set has n elements, then it has 2^n possible subsets.


The <a href = "https://math.stackexchange.com/questions/546414/what-is-the-proof-that-the-total-number-of-subsets-of-a-set-is-2n">proof of this can be done many ways</a>, but the simplest (in my opinion) is to imagine a row of light switches. They can be either on or off. 
If we have n of these switches to represent the n elements of the set, then we have 2*2*2*2*...*2 = 2^n different on/off combos to represent the 2^n subsets.
Note: We can define "on" to mean "include this in the subset", while "off" means "exclude it from the subset".


For instance, let's say we had the set of people code named A,B,C,D
{A,B,C,D} is the original set
Now consider the string 0,1,1,0
0 = off
1 = on
We'll exclude members A and D, while including members B and C
The string 0,1,1,0 leads us to the subset {B, C} which is one of the 2^2 = 4 possible.
Having all zeros gets us the empty set with nothing inside.
Having all ones gets us the original set. Any set is a subset of itself.


With that rule in mind, we can see that there are 6 elements in the set A = {7, 5, 6, H, G, n}
This must mean there are 2^6 = 64 different subsets.
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