How many elements does {5, 6} × P({1, 2, 3}) contain?

Question

The question is: How many elements does {5, 6} × P({1, 2, 3}) contain?

I know if I try every combination, I will get 16. May I know what's the calculation to get the answer quickly?

Answer 1

$A=\{5,6\}$ has 2 elements. $B=\mathcal{P}(\{1,2,3\})$ has $2^3 = 8$ elements.

The cartesian product $A \times B$ has $2 \times 8 = 16$ elements.

Answer 2

Here are the formulas, I bet you can figure it out yourself: $|P(A)| = 2^{|A|}$, $|A \times B| = |A| \cdot |B|$.