{"id":236894,"date":"2025-06-16T15:54:15","date_gmt":"2025-06-16T15:54:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236894"},"modified":"2025-06-16T15:54:16","modified_gmt":"2025-06-16T15:54:16","slug":"what-is-n-in-nc845","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/what-is-n-in-nc845\/","title":{"rendered":"What is\u00a0n\u00a0in\u00a0nC8=45"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

The correct answer is h = 10<\/strong>.<\/p>\n\n\n\n

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

To solve for h in the equation hC8 = 45, we need to use the formula for combinations, which is given by:<\/p>\n\n\n\n

C(n, k) = n! \/ [k!(n – k)!]<\/strong><\/p>\n\n\n\n

where n is the total number of items, k is the number of items chosen, and “!” denotes factorial, which is the product of all positive integers up to that number.<\/p>\n\n\n\n

Substituting h and k = 8 into the equation:<\/p>\n\n\n\n

C(h, 8) = h! \/ [8!(h – 8)!] = 45<\/strong><\/p>\n\n\n\n

Since 8! = 40320, the equation simplifies to:<\/p>\n\n\n\n

h! \/ [40320(h – 8)!] = 45<\/strong><\/p>\n\n\n\n

Multiplying both sides by 40320 gives:<\/p>\n\n\n\n

h! = 45 \u00d7 40320 \u00d7 (h – 8)!<\/strong><\/p>\n\n\n\n

which simplifies further to:<\/p>\n\n\n\n

h! = 1814400 \u00d7 (h – 8)!<\/strong><\/p>\n\n\n\n

Now, we need to determine h such that this equation holds. Testing different values:<\/p>\n\n\n\n

For h = 10:<\/p>\n\n\n\n

10! = 10 \u00d7 9 \u00d7 8! = 3628800<\/strong><\/p>\n\n\n\n

Since 8! cancels out, we have:<\/p>\n\n\n\n

3628800 \/ [8!(10 – 8)!] = 3628800 \/ (2 \u00d7 40320) = 45<\/strong><\/p>\n\n\n\n

Thus, h = 10 satisfies the equation.<\/p>\n\n\n\n

Understanding the Concept<\/h3>\n\n\n\n

Combinations determine how many ways we can select a subset of items from a larger set without considering order. This problem required solving for h in a binomial coefficient equation. By recognizing the factorial pattern, the solution was derived mathematically. The key step was rewriting factorials to isolate h and verify through substitution. Such methods are commonly used in probability theory and combinatorial mathematics to analyze arrangements and selections efficiently.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: The correct answer is h = 10. Explanation To solve for h in the equation hC8 = 45, we need to use the formula for combinations, which is given by: C(n, k) = n! \/ [k!(n – k)!] where n is the total number of items, k is the […]<\/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-236894","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236894","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=236894"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236894\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}