{"id":90259,"date":"2025-06-01T10:24:04","date_gmt":"2025-06-01T10:24:04","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90259"},"modified":"2025-06-01T10:24:04","modified_gmt":"2025-06-01T10:24:04","slug":"the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu\/","title":{"rendered":"The number of ways in which 3 boys and 2 girls can be arranged in a qu"},"content":{"rendered":"

The number of ways in which 3 boys and 2 girls can be arranged in a queue, given that the 2 girls have to be next to each other, is<\/p>\n

[amp_mcq option1=”12″ option2=”24″ option3=”48″ option4=”120″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
We have 3 boys (B) and 2 girls (G). The constraint is that the 2 girls must be next to each other. We can treat the 2 girls as a single combined unit. Now we have 3 boys and this one ‘girl unit’, totaling 4 items to arrange in a queue: B, B, B, (GG). The number of ways to arrange these 4 distinct items (treating the boys as distinct for now, although the problem doesn’t specify, in permutations, items are usually treated as distinct unless stated otherwise) is 4! = 24. However, within the ‘girl unit’ (GG), the two girls can swap positions (G1G2 or G2G1). There are 2! = 2 ways to arrange the 2 girls within their unit. The total number of ways to arrange the 3 boys and 2 girls with the girls together is the product of the number of ways to arrange the 4 items and the number of ways to arrange the girls within their unit. Total ways = 4! * 2! = 24 * 2 = 48.<\/section>\n
To solve permutation problems with a constraint that a group of items must stay together, treat the constrained group as a single unit. Calculate the permutations of the units, and then multiply by the permutations within the constrained unit.<\/section>\n
If the 3 boys were identical and the 2 girls were identical, the approach would be different (involving combinations or partitions), but standard queue arrangement problems typically assume distinct individuals unless otherwise specified.<\/section>\n","protected":false},"excerpt":{"rendered":"

The number of ways in which 3 boys and 2 girls can be arranged in a queue, given that the 2 girls have to be next to each other, is [amp_mcq option1=”12″ option2=”24″ option3=”48″ option4=”120″ correct=”option3″] This question was previously asked in UPSC CAPF – 2018 Download PDFAttempt Online We have 3 boys (B) and … <\/p>\n

Detailed SolutionThe number of ways in which 3 boys and 2 girls can be arranged in a qu<\/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":[1114,1102],"class_list":["post-90259","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1114","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe number of ways in which 3 boys and 2 girls can be arranged in a qu<\/title>\n<meta name=\"description\" content=\"We have 3 boys (B) and 2 girls (G). The constraint is that the 2 girls must be next to each other. We can treat the 2 girls as a single combined unit. Now we have 3 boys and this one 'girl unit', totaling 4 items to arrange in a queue: B, B, B, (GG). The number of ways to arrange these 4 distinct items (treating the boys as distinct for now, although the problem doesn't specify, in permutations, items are usually treated as distinct unless stated otherwise) is 4! = 24. However, within the 'girl unit' (GG), the two girls can swap positions (G1G2 or G2G1). There are 2! = 2 ways to arrange the 2 girls within their unit. The total number of ways to arrange the 3 boys and 2 girls with the girls together is the product of the number of ways to arrange the 4 items and the number of ways to arrange the girls within their unit. Total ways = 4! * 2! = 24 * 2 = 48. To solve permutation problems with a constraint that a group of items must stay together, treat the constrained group as a single unit. Calculate the permutations of the units, and then multiply by the permutations within the constrained unit.\" \/>\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\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The number of ways in which 3 boys and 2 girls can be arranged in a qu\" \/>\n<meta property=\"og:description\" content=\"We have 3 boys (B) and 2 girls (G). The constraint is that the 2 girls must be next to each other. We can treat the 2 girls as a single combined unit. Now we have 3 boys and this one 'girl unit', totaling 4 items to arrange in a queue: B, B, B, (GG). The number of ways to arrange these 4 distinct items (treating the boys as distinct for now, although the problem doesn't specify, in permutations, items are usually treated as distinct unless stated otherwise) is 4! = 24. However, within the 'girl unit' (GG), the two girls can swap positions (G1G2 or G2G1). There are 2! = 2 ways to arrange the 2 girls within their unit. The total number of ways to arrange the 3 boys and 2 girls with the girls together is the product of the number of ways to arrange the 4 items and the number of ways to arrange the girls within their unit. Total ways = 4! * 2! = 24 * 2 = 48. To solve permutation problems with a constraint that a group of items must stay together, treat the constrained group as a single unit. Calculate the permutations of the units, and then multiply by the permutations within the constrained unit.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:24:04+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=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The number of ways in which 3 boys and 2 girls can be arranged in a qu","description":"We have 3 boys (B) and 2 girls (G). The constraint is that the 2 girls must be next to each other. We can treat the 2 girls as a single combined unit. Now we have 3 boys and this one 'girl unit', totaling 4 items to arrange in a queue: B, B, B, (GG). The number of ways to arrange these 4 distinct items (treating the boys as distinct for now, although the problem doesn't specify, in permutations, items are usually treated as distinct unless stated otherwise) is 4! = 24. However, within the 'girl unit' (GG), the two girls can swap positions (G1G2 or G2G1). There are 2! = 2 ways to arrange the 2 girls within their unit. The total number of ways to arrange the 3 boys and 2 girls with the girls together is the product of the number of ways to arrange the 4 items and the number of ways to arrange the girls within their unit. Total ways = 4! * 2! = 24 * 2 = 48. To solve permutation problems with a constraint that a group of items must stay together, treat the constrained group as a single unit. Calculate the permutations of the units, and then multiply by the permutations within the constrained unit.","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\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu\/","og_locale":"en_US","og_type":"article","og_title":"The number of ways in which 3 boys and 2 girls can be arranged in a qu","og_description":"We have 3 boys (B) and 2 girls (G). The constraint is that the 2 girls must be next to each other. We can treat the 2 girls as a single combined unit. Now we have 3 boys and this one 'girl unit', totaling 4 items to arrange in a queue: B, B, B, (GG). The number of ways to arrange these 4 distinct items (treating the boys as distinct for now, although the problem doesn't specify, in permutations, items are usually treated as distinct unless stated otherwise) is 4! = 24. However, within the 'girl unit' (GG), the two girls can swap positions (G1G2 or G2G1). There are 2! = 2 ways to arrange the 2 girls within their unit. The total number of ways to arrange the 3 boys and 2 girls with the girls together is the product of the number of ways to arrange the 4 items and the number of ways to arrange the girls within their unit. Total ways = 4! * 2! = 24 * 2 = 48. To solve permutation problems with a constraint that a group of items must stay together, treat the constrained group as a single unit. Calculate the permutations of the units, and then multiply by the permutations within the constrained unit.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:24:04+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-qu\/","name":"The number of ways in which 3 boys and 2 girls can be arranged in a qu","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:24:04+00:00","dateModified":"2025-06-01T10:24:04+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"We have 3 boys (B) and 2 girls (G). The constraint is that the 2 girls must be next to each other. We can treat the 2 girls as a single combined unit. Now we have 3 boys and this one 'girl unit', totaling 4 items to arrange in a queue: B, B, B, (GG). The number of ways to arrange these 4 distinct items (treating the boys as distinct for now, although the problem doesn't specify, in permutations, items are usually treated as distinct unless stated otherwise) is 4! = 24. However, within the 'girl unit' (GG), the two girls can swap positions (G1G2 or G2G1). There are 2! = 2 ways to arrange the 2 girls within their unit. The total number of ways to arrange the 3 boys and 2 girls with the girls together is the product of the number of ways to arrange the 4 items and the number of ways to arrange the girls within their unit. Total ways = 4! * 2! = 24 * 2 = 48. To solve permutation problems with a constraint that a group of items must stay together, treat the constrained group as a single unit. 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