Let A and B be two sets containing four and two elements respectively.

Question

Let $A$ and $B$ be two sets containing four and two elements respectively. Then the number of subsets of the set $A	imes B$ each having at least three elements is:

Accepted Answer

$n(A\times B) = 4\times2=8$.

$$\sum_{k=3}^{8}\binom8k = 2^8 - \binom80-\binom81-\binom82 = 256-1-8-28 = 219$$

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