{"id":224379,"date":"2025-06-03T04:57:30","date_gmt":"2025-06-03T04:57:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224379"},"modified":"2025-06-03T04:57:32","modified_gmt":"2025-06-03T04:57:32","slug":"if-josh-has-5-different-pairs-of-socks-and-4-different-pairs-of-shoes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/if-josh-has-5-different-pairs-of-socks-and-4-different-pairs-of-shoes\/","title":{"rendered":"If Josh has 5 different pairs of socks and 4 different pairs of shoes"},"content":{"rendered":"\n

If Josh has 5 different pairs of socks and 4 different pairs of shoes, how many different combinations could he wear? 08 O 10 20 18 25<\/p>\n\n\n\n

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

To find the number of different combinations Josh can wear, we need to multiply the number of sock combinations<\/strong> by the number of shoe combinations<\/strong>.<\/p>\n\n\n\n

Step-by-step solution:<\/h3>\n\n\n\n

Josh has:<\/p>\n\n\n\n

    \n
  • 5 different pairs<\/strong> of socks<\/li>\n\n\n\n
  • 4 different pairs<\/strong> of shoes<\/li>\n<\/ul>\n\n\n\n

    Since we’re talking about pairs<\/strong>, each combination refers to one complete pair of socks<\/strong> and one complete pair of shoes<\/strong>. He chooses 1 pair of socks<\/strong> from 5, and 1 pair of shoes<\/strong> from 4.<\/p>\n\n\n\n

    Using the Fundamental Principle of Counting<\/strong>, the total number of combinations is: Total combinations=Number of sock pairs\u00d7Number of shoe pairs=5\u00d74=20\\text{Total combinations} = \\text{Number of sock pairs} \\times \\text{Number of shoe pairs} = 5 \\times 4 = 20<\/p>\n\n\n\n

    \u2705 Correct Answer: 20<\/strong><\/h3>\n\n\n\n
    \n\n\n\n

    Explanation:<\/h3>\n\n\n\n

    This type of problem is a classic example of a combinatorics<\/strong> question, where we are asked to find the total number of outfit combinations<\/strong> Josh can make using different articles of clothing. The key here is understanding that we are combining independent choices<\/strong>: socks and shoes. Each pair of socks can be matched with any<\/strong> pair of shoes, regardless of their style, color, or type.<\/p>\n\n\n\n

    Let\u2019s visualize:
    Suppose the sock pairs are labeled S\u2081, S\u2082, S\u2083, S\u2084, S\u2085, and the shoe pairs are labeled H\u2081, H\u2082, H\u2083, H\u2084.
    If Josh wears S\u2081, he has 4 options for shoes: H\u2081, H\u2082, H\u2083, H\u2084.
    The same goes for S\u2082 through S\u2085. That\u2019s 4 shoe options for each of the 5 sock options.
    So, we calculate: 5 (sock pairs)\u00d74 (shoe pairs)=20 combinations5 \\text{ (sock pairs)} \\times 4 \\text{ (shoe pairs)} = 20 \\text{ combinations}<\/p>\n\n\n\n

    This approach follows the multiplication principle<\/strong>, which states that if one event can happen in m<\/em> ways and another independent event can happen in n<\/em> ways, then the two events together can occur in m \u00d7 n<\/em> ways.<\/p>\n\n\n\n

    This is a foundational principle in mathematics that helps us calculate possibilities without listing every single combination manually.<\/p>\n\n\n\n

    So, with 5 sock choices and 4 shoe choices, Josh has 20 different ways<\/strong> to dress his feet!<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    If Josh has 5 different pairs of socks and 4 different pairs of shoes, how many different combinations could he wear? 08 O 10 20 18 25 The Correct Answer and Explanation is: To find the number of different combinations Josh can wear, we need to multiply the number of sock combinations by the number […]<\/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-224379","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224379","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=224379"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224379\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}