How many license plate having three letters followed by three digits can be made so that all letters and all digits are repeated?<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To calculate how many license plates can be made with the specified conditions, we need to understand the rules for forming the plate.<\/p>\n\n\n\n The license plate consists of three letters followed by three digits. The key part of the question is that all letters and all digits are repeated<\/strong>, which means that the same letter or digit can appear multiple times in the plate. Let\u2019s break it down step by step:<\/p>\n\n\n\n The first three characters of the plate are letters. The English alphabet consists of 26 letters. Since the letters can be repeated, for each of the three letter positions, there are 26 possible choices<\/strong>. Thus, the total number of ways to choose the letters is: 26\u00d726\u00d726=263=17,57626 \\times 26 \\times 26 = 26^3 = 17,576<\/p>\n\n\n\n The next three characters are digits. Digits range from 0 to 9, so there are 10 possible choices<\/strong> for each digit position. Again, since the digits can be repeated, the total number of ways to choose the digits is: 10\u00d710\u00d710=103=1,00010 \\times 10 \\times 10 = 10^3 = 1,000<\/p>\n\n\n\n Since the choices for the letters and digits are independent of each other, we can multiply the total number of ways to choose the letters and digits. Therefore, the total number of possible license plates is: 17,576\u00d71,000=17,576,00017,576 \\times 1,000 = 17,576,000<\/p>\n\n\n\n The total number of license plates that can be made with three letters followed by three digits, where all letters and digits can be repeated, is 17,576,000<\/strong>. This calculation assumes that repetition is allowed for both the letters and the digits, and that each position can independently be any of the 26 letters or 10 digits.<\/p>\n","protected":false},"excerpt":{"rendered":" How many license plate having three letters followed by three digits can be made so that all letters and all digits are repeated? The correct answer and explanation is: To calculate how many license plates can be made with the specified conditions, we need to understand the rules for forming the plate. The license plate […]<\/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-267535","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267535","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=267535"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267535\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=267535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=267535"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=267535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Number of Choices for Letters<\/h3>\n\n\n\n
Step 2: Number of Choices for Digits<\/h3>\n\n\n\n
Step 3: Total Number of License Plates<\/h3>\n\n\n\n
Conclusion<\/h3>\n\n\n\n