To calculate the probability of predicting the first and second horses correctly and in the correct order, we need to consider the number of possible outcomes and the favorable outcomes.<\/p>\n\n\n\n
Step 1: Total Number of Possible Outcomes<\/h3>\n\n\n\n
In a horse race with 6 horses, we are predicting the ranking of all 6 horses. The total number of possible ways the horses can finish in the race is the number of permutations of the 6 horses. The formula for the number of permutations of nnn objects is:P(n)=n!P(n) = n!P(n)=n!<\/p>\n\n\n\n
For 6 horses, the total number of possible outcomes is:P(6)=6!=6\u00d75\u00d74\u00d73\u00d72\u00d71=720P(6) = 6! = 6 \\times 5 \\times 4 \\times 3 \\times 2 \\times 1 = 720P(6)=6!=6\u00d75\u00d74\u00d73\u00d72\u00d71=720<\/p>\n\n\n\n
Step 2: Favorable Outcomes<\/h3>\n\n\n\n
To have the first and second horses correct and in the correct order, we need to focus on the first two positions. We have 6 choices for the first position and 5 remaining choices for the second position (since one horse has already been chosen for the first position). Therefore, the number of favorable outcomes is:6\u00d75=306 \\times 5 = 306\u00d75=30<\/p>\n\n\n\n
Step 3: Probability Calculation<\/h3>\n\n\n\n
Now that we know the total number of possible outcomes (720) and the number of favorable outcomes (30), we can calculate the probability. The probability PPP is the ratio of favorable outcomes to total possible outcomes:P=favorable outcomestotal possible outcomes=30720=124P = \\frac{\\text{favorable outcomes}}{\\text{total possible outcomes}} = \\frac{30}{720} = \\frac{1}{24}P=total possible outcomesfavorable outcomes\u200b=72030\u200b=241\u200b<\/p>\n\n\n\n
Final Answer<\/h3>\n\n\n\n
The probability that you will get the first and second horse correct and in the correct order is:124\\boxed{\\frac{1}{24}}241\u200b\u200b<\/p>\n\n\n\n
Thus, the probability is 124\\frac{1}{24}241\u200b.<\/p>\n\n\n\n In a horse race with 6 horses, you make a bet by predicting the ranking of all 6 horses. If you place your bet at random, what is the probability that you will get the first and second horse correct and in the correct order? Enter your answer as a simplified fraction: To enter your […]<\/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-269981","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269981","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=269981"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269981\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=269981"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=269981"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=269981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1916.jpeg\")
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