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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

Number of ways to seat 5 couples in a row such that each couple sits together:

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.

StartABCBCACAB6 ordered outcomes (permutations); pairing AB/BA etc gives 3 combinations

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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