UPSC CAPF (AC) 2024 Paper I · Question 64

Question 64 of the UPSC CAPF (AC) 2024 Paper I (4 August 2024). Try it first, then open the answer and explanation.

1. CAPF 2024 · P-I · Q64 · General Mental Ability · Arithmetic

   A group of five people consisting of a couple are to be seated on a round table for a meeting. What is the total number of ways in which the seating arrangement can be made so that the couple do NOT sit next to each other?

   1. 24
   2. 18
   3. 12
   4. 6

   पांच व्यक्तियों के एक समूह को, जिसमें एक दंपति (युगल) भी शामिल है, एक बैठक के लिए गोलमेज पर बैठना है। ऐसे तरीकों की कुल संख्या कितनी है, जिनमें बैठने की व्यवस्था ऐसे की जा सके कि दंपति एक दूसरे के बगल में नहीं बैठे?

   1. 24
   2. 18
   3. 12
   4. 6
   Show answer

   Answer: (3) 12

   उत्तर: (3) 12

   Five people can sit round a table in (5 - 1)! = 24 ways. Treating the couple as one unit gives (4 - 1)! × 2 = 12 arrangements with them together, so 24 - 12 = 12 arrangements keep them apart.

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