{"id":6769,"date":"2021-10-21T14:13:49","date_gmt":"2021-10-21T08:43:49","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6769"},"modified":"2021-10-25T01:33:30","modified_gmt":"2021-10-24T20:03:30","slug":"how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/","title":{"rendered":"How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>There are 4 odd digits (1, 1, 3, 3) and 4 odd places(first, third, fifth and seventh).<\/p>\n<p>At these places the odd digits can be arranged in \\(4!\\over 2!2!\\) = 6<\/p>\n<p>Then at the remaining 3 places, the remaining three digits(2, 2, 4) can be arranged in \\(3!\\over 2!\\) = 3 ways<\/p>\n<p>Therefore,\u00a0 The required number of numbers = 6 \\(\\times\\) 3 = 18<\/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\/a-student-is-to-answer-10-out-of-13-questions-in-an-examination-such-that-he-must-choose-atleast-4-from-the-first-five-questions-the-number-of-choices-available-to-him-is\/\" aria-label=\"\u201cA student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is\u201d (Edit)\">A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him 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 : There are 4 odd digits (1, 1, 3, 3) and 4 odd places(first, third, fifth and seventh). At these places the odd digits can be arranged in \\(4!\\over 2!2!\\) = 6 Then at the remaining 3 places, the remaining three digits(2, 2, 4) can be arranged in \\(3!\\over 2!\\) = 3 ways Therefore,\u00a0 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/\"> <span class=\"screen-reader-text\">How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?<\/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>How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?<\/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\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?\" \/>\n<meta property=\"og:description\" content=\"Solution : There are 4 odd digits (1, 1, 3, 3) and 4 odd places(first, third, fifth and seventh). At these places the odd digits can be arranged in (4!over 2!2!) = 6 Then at the remaining 3 places, the remaining three digits(2, 2, 4) can be arranged in (3!over 2!) = 3 ways Therefore,\u00a0 &hellip; How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places? Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T08:43:49+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T20:03:30+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\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?\",\"datePublished\":\"2021-10-21T08:43:49+00:00\",\"dateModified\":\"2021-10-24T20:03:30+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/\"},\"wordCount\":222,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Permutation &amp; 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At these places the odd digits can be arranged in (4!over 2!2!) = 6 Then at the remaining 3 places, the remaining three digits(2, 2, 4) can be arranged in (3!over 2!) = 3 ways Therefore,\u00a0 &hellip; How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places? Read More &raquo;","og_url":"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/","og_site_name":"Mathemerize","article_published_time":"2021-10-21T08:43:49+00:00","article_modified_time":"2021-10-24T20:03:30+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?","datePublished":"2021-10-21T08:43:49+00:00","dateModified":"2021-10-24T20:03:30+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/how-many-numbers-can-be-formed-with-the-digits-1-2-3-4-3-2-1-so-that-the-odd-digits-always-occupy-the-odd-places\/"},"wordCount":222,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Permutation &amp; 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