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Tiga pasang suami istri duduk berdampingan pada satu baris. Jika setiap pasang suami istri harus duduk berdampingan, maka banyak cara mereka duduk adalah \ldots

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Q. Tiga pasang suami istri duduk berdampingan pada satu baris. Jika setiap pasang suami istri harus duduk berdampingan, maka banyak cara mereka duduk adalah \ldots
  1. Calculate Units Arrangement: First, treat each couple as a single unit since they have to sit together. So, we have 33 units to arrange.\newlineCalculate the number of ways to arrange these 33 units: 3!=3×2×1=63! = 3 \times 2 \times 1 = 6.
  2. Calculate Couple Arrangement: Now, within each unit (couple), there are 22 people who can switch places. So for each couple, there are 2!2! ways to arrange them.\newlineCalculate the number of ways to arrange each couple: 2!=2×1=22! = 2 \times 1 = 2.
  3. Calculate Total Arrangements: Since there are 33 couples, and each couple can be arranged in 22 ways, multiply the number of arrangements for each couple: 2×2×2=23=82 \times 2 \times 2 = 2^3 = 8.
  4. Multiply Total Arrangements: Finally, multiply the number of ways to arrange the 33 units (couples) by the number of ways to arrange the people within each unit.\newlineCalculate the total number of arrangements: 66 (ways to arrange units) ×\times 88 (ways to arrange people within units) =48= 48.

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