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89.Subsets with Bold Elements

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combinatoricsCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
Erica intends to construct a subset TT of S={I,J,K,L,M,N}S = \{I, J, K, L, M, N\}, but if she is unsure about including an element xx of SS in TT, she will write xx in bold and include it in TT. For example, {I,J}\{I, \mathbf{J}\}, {J,K,L}\{J, K, \mathbf{L}\}, and {I,J,M,N}\{I, J, M, N\} are valid examples of TT, while {I,J,J,K}\{I, J, \mathbf{J}, K\} is not. Find the total number of such sets TT that Erica can construct.

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