{"id":6941,"date":"2021-10-22T01:51:47","date_gmt":"2021-10-21T20:21:47","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6941"},"modified":"2021-10-25T01:27:36","modified_gmt":"2021-10-24T19:57:36","slug":"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","status":"publish","type":"post","link":"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\/","title":{"rendered":"The set S = {1,2,3,…..,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"},"content":{"rendered":"

Solution :<\/h2>\n

first we choose 4 numbers from 12 numbers, then 4 from remaining 8 numbers, and then 4 from remaining 4 numbers<\/p>\n

So, Required number of ways<\/p>\n

= \\(^{12}C_4\\) x \\(^8C_4\\) x \\(^4C_4\\)<\/p>\n

= \\(12!\\over (4!)^3\\)<\/p>\n

\n

Similar Questions<\/h3>\n

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

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

There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then<\/a><\/p>\n

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

From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that selection contains one of each category is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : first we choose 4 numbers from 12 numbers, then 4 from remaining 8 numbers, and then 4 from remaining 4 numbers So, Required number of ways = \\(^{12}C_4\\) x \\(^8C_4\\) x \\(^4C_4\\) = \\(12!\\over (4!)^3\\) Similar Questions How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in …<\/p>\n

The set S = {1,2,3,…..,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<\/span> Read More »<\/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":"\nThe set S = {1,2,3,.....,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<\/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\/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\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The set S = {1,2,3,.....,12} is to be partitioned into three sets A, B and C of equal size. 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