Solving Combinatorics: Finding the Number of Sets with Elements from A, B, and C

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To determine the number of sets that can be formed using elements from sets A, B, and C, one approach is to simplify the problem by starting with smaller sets, such as A = {a1, a2}, B = {b1, b2}, and C = {c1, c2}. By enumerating the combinations of these smaller sets, a pattern can be identified that may help in generalizing the solution for larger sets. The total number of combinations can be calculated by multiplying the number of elements in each set. This method provides a foundational understanding before exploring more complex combinatorial techniques. Ultimately, this approach aids in solving the problem of counting sets formed from A, B, and C.
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Please help me with combinatorics:
I have three sets:
A with elements (a1 ……..ai )
B with elements (b1 ……..bk )
C with elements (c1 ……..cj )

Pls help me to work out how many sets ABC shall I have that contain each element from sets A, B and C

Thanks much
 
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You can try to simplify the problem first by considering something you can do by simple enumeration with A (a1,a2) B(b1,b2) and C(c1,c2). Then you try to generalize your results. Of course there are better ways, fancier etc but at least you have a starting point.
 
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