How many triples (A, B, C) are there of sets with union A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A ∩ B ∩ C = ∅?
Solution
Answer: 610.
Easy.
Careful. The answer is not 310 (this trap is the only reason I do not rate the problem trivial!).
There are six possibilities for each element: just A, just B, just C, not A (meaning B and C, but not A), not B, or not C.
© John Scholes
jscholes@kalva.demon.co.uk
3 Nov 1999