Finding total no. of subsets

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I tried, but forming even 1 or 2 triplets is easy, but I am not getting how to find this in terms of the power of 100. Can anyone help with this?

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Drawing a venn diagram would help.

So each element 1-100 goes in one of the seven sections.(7^100) But you exclude the cases where there is no element in A intersection B and B intersection C (-2*6^100) and add the case where both A intersection B and B intersection C has no elements (5^100) because those cases have been subtracted twice.