{"id":6771,"date":"2021-10-21T15:28:34","date_gmt":"2021-10-21T09:58:34","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6771"},"modified":"2021-10-25T01:33:37","modified_gmt":"2021-10-24T20:03:37","slug":"in-how-many-ways-can-5-different-mangoes-4-different-oranges-3-different-apples-be-distributed-among-3-children-such-that-each-gets-atleast-one-mango","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-how-many-ways-can-5-different-mangoes-4-different-oranges-3-different-apples-be-distributed-among-3-children-such-that-each-gets-atleast-one-mango\/","title":{"rendered":"In how many ways can 5 different mangoes, 4 different oranges &#038; 3 different apples be distributed among 3 children such that each gets atleast one mango?"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>5 different mangoes can be distributed by following ways among 3 children such that each gets at least 1 :<\/p>\n<p>Total number of ways : (\\(5!\\over 3!1!1!2!\\) + \\(5!\\over 2!2!2!\\)) \\(\\times\\) 3!<\/p>\n<p>Now, the number of ways of distributing remaining fruits (i.e. 4 oranges + 3 apples) among 3 children = \\(3^7\\) (as each fruit has 3 options).<\/p>\n<p>Therefore, Total number of ways = (\\(5!\\over 3!2!\\) + \\(5!\\over {(2!)}^3\\)) \\(\\times\\) 3! \\(\\times\\) \\(3^7\\)<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/how-many-different-words-can-be-formed-by-jumbling-the-letters-in-the-word-mississippi-in-which-no-two-s-are-adjacent\/\" aria-label=\"\u201cHow many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which no two S are adjacent ?\u201d (Edit)\">How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which no two S are adjacent ?<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/from-6-different-novels-and-3-different-dictionaries-4-novels-and-1-dictionary-are-to-be-selected-and-arranged-in-a-row-on-the-shelf-so-that-the-dictionary-is-always-in-the-middle-then-the-number-o\/\" aria-label=\"\u201cFrom 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is\u201d (Edit)\">From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/the-number-of-ways-in-which-6-men-and-5-women-can-dine-at-a-round-table-if-no-two-women-are-to-sit-together-is-given-by\/\" aria-label=\"\u201cThe number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by\u201d (Edit)\">The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/let-t_n-be-the-number-of-all-possible-triangles-formed-by-joining-vertices-of-an-n-sided-regular-polygon-if-t_n1-t_n-10-then-the-value-of-n-is\/\" aria-label=\"\u201cLet \\(T_n\\) be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If \\(T_{n+1}\\) \u2013 \\(T_n\\) = 10, then the value of n is\u201d (Edit)\">Let \\(T_n\\) be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If \\(T_{n+1}\\) \u2013 \\(T_n\\) = 10, then the value of n is<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/the-set-s-123-12-is-to-be-partitioned-into-three-sets-a-b-and-c-of-equal-size-thus-acup-bcup-c-s-acap-b-bcap-c-acap-c-phi-the-number-of\/\" aria-label=\"\u201cThe set S = {1,2,3,\u2026..,12} is to be partitioned into three sets A, B and C of equal size. Thus, \\(A\\cup B\\cup C\\) = S \\(A\\cap B\\) = \\(B\\cap C\\) = \\(A\\cap C\\) = \\(\\phi\\) The number of ways to partition S is\u201d (Edit)\">The set S = {1,2,3,\u2026..,12} is to be partitioned into three sets A, B and C of equal size. Thus, \\(A\\cup B\\cup C\\) = S \\(A\\cap B\\) = \\(B\\cap C\\) = \\(A\\cap C\\) = \\(\\phi\\) The number of ways to partition S is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : 5 different mangoes can be distributed by following ways among 3 children such that each gets at least 1 : Total number of ways : (\\(5!\\over 3!1!1!2!\\) + \\(5!\\over 2!2!2!\\)) \\(\\times\\) 3! Now, the number of ways of distributing remaining fruits (i.e. 4 oranges + 3 apples) among 3 children = \\(3^7\\) (as &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/in-how-many-ways-can-5-different-mangoes-4-different-oranges-3-different-apples-be-distributed-among-3-children-such-that-each-gets-atleast-one-mango\/\"> <span class=\"screen-reader-text\">In how many ways can 5 different mangoes, 4 different oranges &#038; 3 different apples be distributed among 3 children such that each gets atleast one mango?<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,47],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>In how many ways can 5 different mangoes, 4 different oranges &amp; 3 different apples be distributed among 3 children such that each gets atleast one mango?<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/in-how-many-ways-can-5-different-mangoes-4-different-oranges-3-different-apples-be-distributed-among-3-children-such-that-each-gets-atleast-one-mango\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In how many ways can 5 different mangoes, 4 different oranges &amp; 3 different apples be distributed among 3 children such that each gets atleast one mango?\" \/>\n<meta property=\"og:description\" content=\"Solution : 5 different mangoes can be distributed by following ways among 3 children such that each gets at least 1 : Total number of ways : ((5!over 3!1!1!2!) + (5!over 2!2!2!)) (times) 3! Now, the number of ways of distributing remaining fruits (i.e. 4 oranges + 3 apples) among 3 children = (3^7) (as &hellip; In how many ways can 5 different mangoes, 4 different oranges &#038; 3 different apples be distributed among 3 children such that each gets atleast one mango? Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/in-how-many-ways-can-5-different-mangoes-4-different-oranges-3-different-apples-be-distributed-among-3-children-such-that-each-gets-atleast-one-mango\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T09:58:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T20:03:37+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/in-how-many-ways-can-5-different-mangoes-4-different-oranges-3-different-apples-be-distributed-among-3-children-such-that-each-gets-atleast-one-mango\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/in-how-many-ways-can-5-different-mangoes-4-different-oranges-3-different-apples-be-distributed-among-3-children-such-that-each-gets-atleast-one-mango\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"In how many ways can 5 different mangoes, 4 different oranges &#038; 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