Answer: 5! × 2⁵.
- A 5! × 2⁵
- B 5! × 2⁴
- C 4! × 2⁵
- D 10!
Correct answer: A. 5! × 2⁵
Explanation: Block method: treat each couple as 1 unit → 5 blocks arranged in 5! = 120 ways. Each couple can swap internally: 2 ways each → 2⁵ = 32. Total = 120×32 = 3840 = 5!×2⁵.
Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.
Concept context
Counting, arrangements, and selections