Step-by-step Solution:

\[ A \cup B = \{1, 2, 3, 4, 5\} \] \[ A \cap B = \{3, 4\} \] \[ A \Delta B = (A - B) \cup (B - A) = \{1, 2, 5\} \] Hence, the number of elements in \((A \cup B) \times (A \cap B) \times (A \Delta B)\) is: \[ 5 \times 2 \times 3 = 30 \]