{"id":166538,"date":"2024-11-13T21:40:59","date_gmt":"2024-11-13T21:40:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=166538"},"modified":"2024-11-13T21:41:01","modified_gmt":"2024-11-13T21:41:01","slug":"a-lady-has-4-dresses-and-she-want-to-leave-2-of-them-behind-and-bring-the-rest-with-her-on-the-trip","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/13\/a-lady-has-4-dresses-and-she-want-to-leave-2-of-them-behind-and-bring-the-rest-with-her-on-the-trip\/","title":{"rendered":"A lady has 4 dresses and she want to leave 2 of them behind and bring the rest with her on the trip."},"content":{"rendered":"\n

A lady has 4 dresses and she want to leave 2 of them behind and bring the rest with her on the trip. How many ways are there for the lady bring dresses with her?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The problem involves choosing 2 dresses to leave behind out of 4 dresses, meaning the lady will bring the remaining 2 dresses with her. This is a classic example of a combination problem because the order in which the dresses are chosen does not matter, only which dresses are selected.<\/p>\n\n\n\n

Step 1: Understand the Problem<\/h3>\n\n\n\n

The lady has 4 dresses, and she wants to bring 2 of them on the trip. To do this, she will leave 2 dresses behind. The task is to determine in how many ways she can choose 2 dresses to leave behind (which is equivalent to choosing 2 dresses to bring with her). This is a selection problem where the order does not matter.<\/p>\n\n\n\n

Step 2: Applying the Combination Formula<\/h3>\n\n\n\n

The number of ways to choose ( r ) objects from ( n ) objects without regard to the order is given by the combination formula:<\/p>\n\n\n\n

[
C(n, r) = \\frac{n!}{r!(n – r)!}
]<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n

    \n
  • ( n ) is the total number of objects (in this case, 4 dresses),<\/li>\n\n\n\n
  • ( r ) is the number of objects to choose (in this case, 2 dresses to leave behind).<\/li>\n<\/ul>\n\n\n\n

    So, the number of ways the lady can choose which 2 dresses to leave behind is:<\/p>\n\n\n\n

    [
    C(4, 2) = \\frac{4!}{2!(4 – 2)!} = \\frac{4!}{2!2!} = \\frac{4 \\times 3 \\times 2!}{2! \\times 2!} = \\frac{12}{4} = 6
    ]<\/p>\n\n\n\n

    Step 3: Interpretation of the Result<\/h3>\n\n\n\n

    Thus, the number of ways the lady can leave 2 dresses behind and bring the other 2 dresses with her is 6<\/strong>. This means there are 6 different combinations of 2 dresses she could leave behind.<\/p>\n\n\n\n

    Step 4: Verifying by Listing Combinations<\/h3>\n\n\n\n

    To further understand, we can list all the possible ways she can leave 2 dresses behind:<\/p>\n\n\n\n

      \n
    • Leave behind dresses 1 and 2, bring 3 and 4.<\/li>\n\n\n\n
    • Leave behind dresses 1 and 3, bring 2 and 4.<\/li>\n\n\n\n
    • Leave behind dresses 1 and 4, bring 2 and 3.<\/li>\n\n\n\n
    • Leave behind dresses 2 and 3, bring 1 and 4.<\/li>\n\n\n\n
    • Leave behind dresses 2 and 4, bring 1 and 3.<\/li>\n\n\n\n
    • Leave behind dresses 3 and 4, bring 1 and 2.<\/li>\n<\/ul>\n\n\n\n

      Thus, the total number of ways is indeed 6.<\/p>\n\n\n\n

      Conclusion<\/h3>\n\n\n\n

      Therefore, there are 6<\/strong> ways for the lady to choose which 2 dresses to leave behind and bring the other 2 with her on her trip. This is a combination problem where the order of selection does not matter.<\/p>\n","protected":false},"excerpt":{"rendered":"

      A lady has 4 dresses and she want to leave 2 of them behind and bring the rest with her on the trip. How many ways are there for the lady bring dresses with her? The Correct Answer and Explanation is: The problem involves choosing 2 dresses to leave behind out of 4 dresses, meaning […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-166538","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166538","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=166538"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166538\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166538"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}