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How many subsets of {1, 2, 3, 4, 5, 6, 7, 8} contain 1, 2, or 5?

 May 16, 2020
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If you consider each number a switch with an in or out, then there are 2^8 = 256 subsets of the set because each number is either in or out. Now we use complementary counting. If we want to count the number of subsets with 1,2 or 5, we can also count the number of subsets without any of those and subtract that count from the total. This count is 2^5 = 32 because 1,2, and 5 have to be out so there are only 5 switches. 256 - 32 = 224

 May 16, 2020

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