Three sets, $\mathbb A$ , $\mathbb B$ and $\mathbb C$ , have 3, 12, and 13 elements respectively. The set $\mathbb D$ is defined as:

$\mathbb D = \{(x,y,z) \mid x \in\mathbb A, y \in\mathbb B, z \in\mathbb C\}$

How many elements does $\mathbb D$ have?

The answer is 468.

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Set $\mathbb D$ is defined as the set of triplets $(x,y,z)$ where $x$ belongs to $\mathbb A$ , $y$ belongs to $\mathbb B$ , and $z$ belongs to $\mathbb C$ , There are 3 elements in $\mathbb A$ , 12 elements in $\mathbb B$ , 13 elements in $\mathbb C$ . There are 3 possibilities for $x$ , 12 possibilities for $y$ , and 13 possibilities for $z$ . So therefore there are:

$3\times 12\times 13 = \boxed {468} \text{ Elements in } \mathbb D$