Step-by-Step Solution
Key Concept: Use permutation formulas for selecting and arranging distinct elements from different sets.
The number of ways is calculated as $^4P_2 \times ^6P_3 \times 15 = 172800$, where $^4P_2$ and $^6P_3$ represent permutations of subsets and 15 is an additional multiplier.
Correct Answer: 1