{"id":55809,"date":"2020-10-01T09:11:00","date_gmt":"2020-10-01T03:41:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=55809"},"modified":"2020-10-05T10:08:37","modified_gmt":"2020-10-05T04:38:37","slug":"ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\/","title":{"rendered":"NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-55601\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/09\/NCERT-Solutions-for-Class-11-Maths-Chapter-7.jpg\" alt=\"NCERT-Solutions-for-Class-11-Maths-Chapter-7\" width=\"785\" height=\"400\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/09\/NCERT-Solutions-for-Class-11-Maths-Chapter-7.jpg 785w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/09\/NCERT-Solutions-for-Class-11-Maths-Chapter-7-768x391.jpg 768w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/09\/NCERT-Solutions-for-Class-11-Maths-Chapter-7-30x15.jpg 30w\" sizes=\"(max-width: 785px) 100vw, 785px\" \/><\/p>\n<p>NCERT solutions for class 11 maths chapter 7 are prepared as per the CBSE guidelines. Permutation is defined as several possible for arranging a set or number of things. The expression to denote permutation is <sup>n<\/sup>P<sub>r<\/sub>. Combinations means the selection of all or part of a set of objects, irrespective of the order in which objects are selected.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-ncert-solutions\/\" target=\"_blank\" rel=\"noopener noreferrer\">NCERT Solutions For 11th Maths All Chapters<\/a><\/li>\n<\/ul>\n<p>There are four exercises &amp; a miscellaneous exercise in this chapter that assists the students to understand the concepts related to Permutations and Combinations clearly.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69e2af93649ad\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69e2af93649ad\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\/#ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\" title=\"NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination\">NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\/#what-will-you-learn-in-cbse-class-11-maths-chapter-7-permutation-and-combination\" title=\"What will you learn in CBSE Class 11 Maths Chapter 7 Permutation and Combination?\">What will you learn in CBSE Class 11 Maths Chapter 7 Permutation and Combination?<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\/#-excercise-wise-questions\" title=\"\u00a0Excercise wise questions:\">\u00a0Excercise wise questions:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\/#theorems-and-formulaes-used-in-chapter\" title=\"Theorems and formulaes used in chapter\">Theorems and formulaes used in chapter<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\"><\/span>NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The students learn about the Permutation and Combination in detail that enables them to score full marks from this chapter by practicing the solutions for all the problems available in the NCERT textbook. The students can conveniently download NCERT solutions for class 11 maths chapter 7 PDF that also boosts their confidence and reduces their fear of final examination.<\/p>\n<p>NCERT class 11 maths chapter 7 solutions are prepared by the subject experts &amp; cover all the exercise questions included in the NCERT textbook. These solutions assist the students while doing their homework.<\/p>\n<p>You can download\u00a0CBSE NCERT Solutions for Class 11 Maths\u00a0Chapter 7 Permutation and Combination\u00a0from below.<\/p>\n<p style=\"margin-top: 24px; text-align: center;\"><a style=\"display: inline-block; width: auto; padding: 18px; cursor: pointer; font-weight: bold; border-radius: 40px; text-decoration-line: underline; color: #ffffff; background: #ff4500; box-shadow: rgba(0, 0, 0, 0.25) 0px 2px 6px 0px;\" href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2020\/10\/NCERT-Solutions-for-Class-11-Maths-Chapter-7.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Download NCERT Class 11 Maths Chapter 7 Solutions<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"what-will-you-learn-in-cbse-class-11-maths-chapter-7-permutation-and-combination\"><\/span>What will you learn in CBSE Class 11 Maths Chapter 7 Permutation and Combination?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Class 11 Maths Chapter 7 Permutations and Combinations is a part of the unit Algebra that adds up to 30 marks of the total 80 marks. The students will learn basic counting techniques &amp; the most fundamental to the learning of these techniques in this chapter. They will learn about Factorial notation where n! represents the product of first n natural numbers i.e the product of 1 \u00d7 2 \u00d7 3 \u00d7 . . . \u00d7 (n \u2013 1) \u00d7 n is denoted as n!.<\/p>\n<p>The Combination is based on a selection of objects &amp; creating a group without considering their mutual ordering. There are four exercises &amp; a miscellaneous exercise in this chapter that assist the students to understand the concepts related to Permutations and Combinations clearly.<\/p>\n<p>The major concepts of Maths covered in chapter 7 solutions are:<\/p>\n<ul>\n<li>1 Introduction<\/li>\n<li>2 Fundamental Principle of Counting<\/li>\n<li>3 Permutations<\/li>\n<li>3.1 Permutations when all the objects are distinct<\/li>\n<li>3.2 Factorial notation<\/li>\n<li>3.3 Derivation of the formula for <sup>n<\/sup>P<sub>r<\/sub><\/li>\n<li>3.4 Permutations when all the objects are not distinct objects<\/li>\n<li>4 Combinations<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"-excercise-wise-questions\"><\/span>\u00a0Excercise wise questions:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Class 11 Maths chapter 7 exercise 7.1 solutions &#8211; 6 Questions<\/li>\n<li>Class 11 Maths chapter 7 exercise 7. 2 solutions &#8211; 5 Questions<\/li>\n<li>Exercise 7.3 solutions for class 11 Maths Chapter 7 9 Questions<\/li>\n<li>Class 11 Maths chapter 7 exercise 7.4 solutions \u2013 10 questions<\/li>\n<li>Class 11 Maths chapter 7 miscellaneous exercise solutions \u2013 11 questions<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"theorems-and-formulaes-used-in-chapter\"><\/span>Theorems and formulaes used in chapter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Permutation formula = <strong>P<sub>r<\/sub>\u00a0= n!\/(n-r)! ; 0\u00a0\u2264 r \u2264 n<\/strong><\/p>\n<p><strong>Combination formula = <sub>n<\/sub>C<sub>r<\/sub>\u00a0= n(n-1)(n-2)\u2026(n-r+1)\/ r! = n!\/ r!(n-r)!=\u00a0<sub>n<\/sub>P<sub>r<\/sub>\u00a0\/r!<\/strong><\/p>\n<p>n! = 1 \u00d7 2 \u00d7 3 \u00d7 \u2026\u00d7n<\/p>\n<p>n! = n \u00d7 (n \u2013 1) !<\/p>\n<p>Theorems<\/p>\n<p><strong>Theorem 1:\u00a0<\/strong><\/p>\n<p>When the number of permutations of n different objects are taken r at a time, the condition is 0 &lt; r \u2264 n and the objects that do not repeat = n ( n \u2013 1) ( n \u2013 2)\u2026\u2026( n \u2013 r + 1). So, the notation that denote the permutation is <sup>n\u00a0<\/sup>P<sub>r<\/sub><\/p>\n<p><strong>Theorem 2: <\/strong><\/p>\n<p>The number of permutations of different objects n are taken r at a time &amp; if repetition is allowed, it is n<sup>r<\/sup>\u00a0.<\/p>\n<p><strong>Theorem 3<\/strong>:<\/p>\n<p>If want to find the number of permutations of the objects n and p are the objects of the same kind and remaining are all different, it is n! \/ p!<\/p>\n<p><strong>Theorem 4<\/strong>:<\/p>\n<p>The number of permutations of n objects if p<sub>1<\/sub>\u00a0are the objects of one kind &amp; p<sub>2<\/sub>\u00a0are the objects of the second kind.<\/p>\n<p>p<sub>k\u00a0<\/sub>is of the k<sup>th<\/sup>\u00a0kind and the remaining are of a different kind then the permutation is n! \/ (p<sub>1<\/sub>!p<sub>2<\/sub>!\u2026P<sub>k<\/sub>!)<\/p>\n<p><strong>Theorem 5<\/strong>:\u00a0<\/p>\n<p>If 0 &lt; r \u2264 n.<\/p>\n<p><sup>n<\/sup>P<sub>r <\/sub>\u00a0=\u00a0 \u00a0<sup>n<\/sup>C<sub>r\u00a0<\/sub>r!<\/p>\n<p><strong>Theorem 6:<\/strong><\/p>\n<p><strong>\u00a0<sup>n<\/sup><\/strong>C<sub>r\u00a0<\/sub>+\u00a0<sup>n<\/sup>C<sub>r-1<\/sub>\u00a0=\u00a0<sup>n+1<\/sup>C<sub>r<\/sub><\/p>\n<p>\u00a0<\/p>\n<p>We have covered the complete guide on\u00a0<a href=\"http:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">CBSE<\/a>\u00a0NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination. Feel free to ask us any questions in the comment section below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT solutions for class 11 maths chapter 7 are prepared as per the CBSE guidelines. Permutation is defined as several possible for arranging a set or number of things. The expression to denote permutation is nPr. Combinations means the selection of all or part of a set of objects, irrespective of the order in which &#8230; <a title=\"NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-11-maths-chapter-7-permutation-and-combination\/\" aria-label=\"More on NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":55601,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2934],"tags":[3428],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/55809"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=55809"}],"version-history":[{"count":0,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/55809\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/55601"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=55809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=55809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=55809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}