{"id":6852,"date":"2021-10-21T21:02:58","date_gmt":"2021-10-21T15:32:58","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6852"},"modified":"2021-10-25T01:31:13","modified_gmt":"2021-10-24T20:01:13","slug":"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","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/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\/","title":{"rendered":"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"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>n(S) = \\(^{10}C_4\\) = 210<\/p>\n<p>n(E)= \\(^5C_2 \\times ^3C_1 \\times ^2C_1\\) + \\(^5C_1 \\times ^3C_2 \\times ^2C_1\\) + \\(^5C_1 \\times ^3C_1 \\times ^2C_2\\) = 105<\/p>\n<p>\\(\\therefore\\) P(E) = \\(105\\over 210\\) = \\(1\\over 2\\)<\/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\/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\/\" aria-label=\"\u201cThere 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\u201d (Edit)\">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<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 : n(S) = \\(^{10}C_4\\) = 210 n(E)= \\(^5C_2 \\times ^3C_1 \\times ^2C_1\\) + \\(^5C_1 \\times ^3C_2 \\times ^2C_1\\) + \\(^5C_1 \\times ^3C_1 \\times ^2C_2\\) = 105 \\(\\therefore\\) P(E) = \\(105\\over 210\\) = \\(1\\over 2\\) Similar Questions How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which no &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/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\/\"> <span class=\"screen-reader-text\">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<\/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>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<\/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\/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\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"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\" \/>\n<meta property=\"og:description\" content=\"Solution : n(S) = (^{10}C_4) = 210 n(E)= (^5C_2 times ^3C_1 times ^2C_1) + (^5C_1 times ^3C_2 times ^2C_1) + (^5C_1 times ^3C_1 times ^2C_2) = 105 (therefore) P(E) = (105over 210) = (1over 2) Similar Questions How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which no &hellip; From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. 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The probability that selection contains one of each category is","og_description":"Solution : n(S) = (^{10}C_4) = 210 n(E)= (^5C_2 times ^3C_1 times ^2C_1) + (^5C_1 times ^3C_2 times ^2C_1) + (^5C_1 times ^3C_1 times ^2C_2) = 105 (therefore) P(E) = (105over 210) = (1over 2) Similar Questions How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which no &hellip; From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. 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