{"id":90984,"date":"2025-06-01T10:42:31","date_gmt":"2025-06-01T10:42:31","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90984"},"modified":"2025-06-01T10:42:31","modified_gmt":"2025-06-01T10:42:31","slug":"a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/","title":{"rendered":"A group of five people consisting of a couple are to be seated on a ro"},"content":{"rendered":"

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 ?<\/p>\n

[amp_mcq option1=”24″ option2=”18″ option3=”12″ option4=”6″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is C.
\n<\/section>\n
\nThere are 5 people in total to be seated around a round table.
\nTotal number of ways to arrange 5 distinct people around a round table is (5-1)! = 4! = 24.<\/p>\n

We want to find the number of ways the couple do NOT sit next to each other. This can be found by subtracting the number of arrangements where the couple *do* sit together from the total number of arrangements.<\/p>\n

To find the number of arrangements where the couple sit together, treat the couple as a single unit.
\nNow we are arranging 4 units around the table: the couple unit + the other 3 individuals.
\nThe number of ways to arrange these 4 units around a round table is (4-1)! = 3! = 6.
\nWithin the couple unit, the two individuals (let’s call them P1 and P2) can sit in two ways: P1-P2 or P2-P1. This can be done in 2! = 2 ways.<\/p>\n

So, the total number of arrangements where the couple sit together is the number of ways to arrange the 4 units multiplied by the number of ways the couple can be arranged within their unit: 6 * 2 = 12.<\/p>\n

The number of ways the couple do NOT sit next to each other is:
\nTotal arrangements – Arrangements where the couple sit together
\n= 24 – 12 = 12.
\n<\/section>\n

\nFor linear arrangements, the total ways for n people is n!. The ways for a specific couple to sit together is (n-1)! * 2!. The ways for them not to sit together is n! – (n-1)! * 2! = n! – 2(n-1)! = n(n-1)! – 2(n-1)! = (n-2)(n-1)!.
\nFor round table arrangements, the total ways for n people is (n-1)!. The ways for a specific couple to sit together is (n-2)! * 2!. The ways for them not to sit together is (n-1)! – (n-2)! * 2! = (n-1)(n-2)! – 2(n-2)! = (n-1-2)(n-2)! = (n-3)(n-2)!.
\nIn this case, n=5.
\nTotal round table arrangements = (5-1)! = 4! = 24.
\nCouple sit together = (5-2)! * 2! = 3! * 2 = 6 * 2 = 12.
\nCouple do not sit together = (5-3)(5-2)! = 2 * 3! = 2 * 6 = 12.
\nThe formula matches the calculation: (n-3)(n-2)! = (5-3)(5-2)! = 2 * 3! = 12.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

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 ? [amp_mcq option1=”24″ option2=”18″ option3=”12″ option4=”6″ correct=”option3″] This question … <\/p>\n

Detailed SolutionA group of five people consisting of a couple are to be seated on a ro<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1103,1102],"class_list":["post-90984","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1103","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA group of five people consisting of a couple are to be seated on a ro<\/title>\n<meta name=\"description\" content=\"The correct option is C. There are 5 people in total to be seated around a round table. Total number of ways to arrange 5 distinct people around a round table is (5-1)! = 4! = 24. We want to find the number of ways the couple do NOT sit next to each other. This can be found by subtracting the number of arrangements where the couple *do* sit together from the total number of arrangements. To find the number of arrangements where the couple sit together, treat the couple as a single unit. Now we are arranging 4 units around the table: the couple unit + the other 3 individuals. The number of ways to arrange these 4 units around a round table is (4-1)! = 3! = 6. Within the couple unit, the two individuals (let's call them P1 and P2) can sit in two ways: P1-P2 or P2-P1. This can be done in 2! = 2 ways. So, the total number of arrangements where the couple sit together is the number of ways to arrange the 4 units multiplied by the number of ways the couple can be arranged within their unit: 6 * 2 = 12. The number of ways the couple do NOT sit next to each other is: Total arrangements - Arrangements where the couple sit together = 24 - 12 = 12.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A group of five people consisting of a couple are to be seated on a ro\" \/>\n<meta property=\"og:description\" content=\"The correct option is C. There are 5 people in total to be seated around a round table. Total number of ways to arrange 5 distinct people around a round table is (5-1)! = 4! = 24. We want to find the number of ways the couple do NOT sit next to each other. This can be found by subtracting the number of arrangements where the couple *do* sit together from the total number of arrangements. To find the number of arrangements where the couple sit together, treat the couple as a single unit. Now we are arranging 4 units around the table: the couple unit + the other 3 individuals. The number of ways to arrange these 4 units around a round table is (4-1)! = 3! = 6. Within the couple unit, the two individuals (let's call them P1 and P2) can sit in two ways: P1-P2 or P2-P1. This can be done in 2! = 2 ways. So, the total number of arrangements where the couple sit together is the number of ways to arrange the 4 units multiplied by the number of ways the couple can be arranged within their unit: 6 * 2 = 12. The number of ways the couple do NOT sit next to each other is: Total arrangements - Arrangements where the couple sit together = 24 - 12 = 12.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:42:31+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A group of five people consisting of a couple are to be seated on a ro","description":"The correct option is C. There are 5 people in total to be seated around a round table. Total number of ways to arrange 5 distinct people around a round table is (5-1)! = 4! = 24. We want to find the number of ways the couple do NOT sit next to each other. This can be found by subtracting the number of arrangements where the couple *do* sit together from the total number of arrangements. To find the number of arrangements where the couple sit together, treat the couple as a single unit. Now we are arranging 4 units around the table: the couple unit + the other 3 individuals. The number of ways to arrange these 4 units around a round table is (4-1)! = 3! = 6. Within the couple unit, the two individuals (let's call them P1 and P2) can sit in two ways: P1-P2 or P2-P1. This can be done in 2! = 2 ways. So, the total number of arrangements where the couple sit together is the number of ways to arrange the 4 units multiplied by the number of ways the couple can be arranged within their unit: 6 * 2 = 12. The number of ways the couple do NOT sit next to each other is: Total arrangements - Arrangements where the couple sit together = 24 - 12 = 12.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/","og_locale":"en_US","og_type":"article","og_title":"A group of five people consisting of a couple are to be seated on a ro","og_description":"The correct option is C. There are 5 people in total to be seated around a round table. Total number of ways to arrange 5 distinct people around a round table is (5-1)! = 4! = 24. We want to find the number of ways the couple do NOT sit next to each other. This can be found by subtracting the number of arrangements where the couple *do* sit together from the total number of arrangements. To find the number of arrangements where the couple sit together, treat the couple as a single unit. Now we are arranging 4 units around the table: the couple unit + the other 3 individuals. The number of ways to arrange these 4 units around a round table is (4-1)! = 3! = 6. Within the couple unit, the two individuals (let's call them P1 and P2) can sit in two ways: P1-P2 or P2-P1. This can be done in 2! = 2 ways. So, the total number of arrangements where the couple sit together is the number of ways to arrange the 4 units multiplied by the number of ways the couple can be arranged within their unit: 6 * 2 = 12. The number of ways the couple do NOT sit next to each other is: Total arrangements - Arrangements where the couple sit together = 24 - 12 = 12.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:42:31+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/","name":"A group of five people consisting of a couple are to be seated on a ro","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:42:31+00:00","dateModified":"2025-06-01T10:42:31+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct option is C. There are 5 people in total to be seated around a round table. Total number of ways to arrange 5 distinct people around a round table is (5-1)! = 4! = 24. We want to find the number of ways the couple do NOT sit next to each other. This can be found by subtracting the number of arrangements where the couple *do* sit together from the total number of arrangements. To find the number of arrangements where the couple sit together, treat the couple as a single unit. Now we are arranging 4 units around the table: the couple unit + the other 3 individuals. The number of ways to arrange these 4 units around a round table is (4-1)! = 3! = 6. Within the couple unit, the two individuals (let's call them P1 and P2) can sit in two ways: P1-P2 or P2-P1. This can be done in 2! = 2 ways. So, the total number of arrangements where the couple sit together is the number of ways to arrange the 4 units multiplied by the number of ways the couple can be arranged within their unit: 6 * 2 = 12. The number of ways the couple do NOT sit next to each other is: Total arrangements - Arrangements where the couple sit together = 24 - 12 = 12.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-group-of-five-people-consisting-of-a-couple-are-to-be-seated-on-a-ro\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"A group of five people consisting of a couple are to be seated on a ro"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90984","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90984"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90984\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90984"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90984"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90984"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}