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An-old-unsolved-question-1132-let-S-1-2-3-4-5-if-A-B-C-is-such-that-A-B-C-A-B-A-C-how-many-ways-can-be-choose-A-B-and-C-




Question Number 163939 by Rasheed.Sindhi last updated on 12/Jan/22
An old unsolved question#1132  let S={1,2,3,4,5}, if A,B,C is such that  A∩B∩C=∅  A∩B≠∅  A∩C≠∅  how many ways can be choose A,B and  C
$$\mathrm{An}\:\mathrm{old}\:\mathrm{unsolved}\:\mathrm{question}#\mathrm{1132} \\ $$$$\mathrm{let}\:\mathrm{S}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\},\:\mathrm{if}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{A}\cap\mathrm{B}\cap\mathrm{C}=\varnothing \\ $$$$\mathrm{A}\cap\mathrm{B}\neq\varnothing \\ $$$$\mathrm{A}\cap\mathrm{C}\neq\varnothing \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{be}\:\mathrm{choose}\:\mathrm{A},\mathrm{B}\:\mathrm{and} \\ $$$$\mathrm{C} \\ $$

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