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

[Neitrino]

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

 

[epsi00]

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.