{"id":6934,"date":"2021-10-22T01:44:25","date_gmt":"2021-10-21T20:14:25","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6934"},"modified":"2021-10-25T01:30:07","modified_gmt":"2021-10-24T20:00:07","slug":"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","status":"publish","type":"post","link":"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\/","title":{"rendered":"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"},"content":{"rendered":"

Solution :<\/h2>\n

If out of n points,\u00a0 m are collinear, then<\/p>\n

Number of triangles = \\(^nC_3\\) – \\(^mC_3\\)<\/p>\n

\\(\\therefore\\)\u00a0 Number of triangles = \\(^{10}C_3\\) – \\(^6C_3\\)<\/p>\n

= 120 – 20<\/p>\n

= 100<\/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

If all the letters of the word \u2018RAPID\u2019 are arranged in all possible manner as they are in a dictionary, then find the rank of the word \u2018RAPID\u2019.<\/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 : If out of n points,\u00a0 m are collinear, then Number of triangles = \\(^nC_3\\) – \\(^mC_3\\) \\(\\therefore\\)\u00a0 Number of triangles = \\(^{10}C_3\\) – \\(^6C_3\\) = 120 – 20 = 100 Similar Questions How many different words can be formed by jumbling the letters in the word \u2018MISSISSIPPI\u2019 in which no two S are …<\/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<\/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":"\nThere are 10 points in a plane, out of these 6 are collinear. 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