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Discrete math Subsets Contained

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Hello,

I have another discrete problem I need help on.

It says: How many subsets contain 1 or 2 or 3 in the set {1,2,...,20}?

So my teacher told me that {1} is a subset, {1,3,4,5,19} would be a subset (i just chose that randomly), {2} would be a subset, {2,5,6,7,20} would be a subset (again, i just chose that at random, and continue to do that for all possible cominations.

I'm just not sure how to find the combinations. I don't think the numbers can be repeated.

So, i'm thinking that say for the number 3,.. would you have 17! possible combinations?
Because you would have
{3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,}
But...then you would have sets like
{3,4,5,6,17,18,20}

uhg...i dont understand. If you guys don't either, no worries, this stuff is hard!

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The expert examines discrete math subsets contained.

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How many subsets contain 1 or 2 or 3 in the set {1,2,...,20}?
Solution
Subsets contain 1 element:
{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {12}, {13}, {14}, {15}, {16}, {17}, ...

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