{"id":90978,"date":"2025-06-01T10:42:24","date_gmt":"2025-06-01T10:42:24","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90978"},"modified":"2025-06-01T10:42:24","modified_gmt":"2025-06-01T10:42:24","slug":"out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/","title":{"rendered":"Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers"},"content":{"rendered":"

Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers can be formed without repetition of digits ?<\/p>\n

[amp_mcq option1=”6″ option2=”15″ option3=”30″ option4=”40″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\n30 two-digit numbers can be formed without repetition of digits.
\n<\/section>\n
\nThe given digits are 1, 2, 3, 4, 5, and 6. There are a total of 6 distinct digits.
\nWe need to form two-digit numbers without repetition. A two-digit number has a tens digit and a units digit.
\nFor the tens digit, we can choose any of the 6 available digits. So, there are 6 choices for the tens digit.
\nSince repetition of digits is not allowed, the units digit must be different from the digit chosen for the tens place. After choosing one digit for the tens place, there are 5 digits remaining. So, there are 5 choices for the units digit.
\nThe total number of two-digit numbers that can be formed is the product of the number of choices for each position:
\nTotal number of numbers = (Number of choices for tens digit) $\\times$ (Number of choices for units digit)
\nTotal number = $6 \\times 5 = 30$.
\n<\/section>\n
\nThis problem is a case of permutation, specifically finding the number of permutations of 6 distinct items taken 2 at a time, denoted as P(6, 2) or $_6P_2$. The formula for permutations is $P(n, k) = \\frac{n!}{(n-k)!}$, where n is the total number of items and k is the number of items to choose.
\nHere, n = 6 (the digits) and k = 2 (the number of digits in the number).
\n$P(6, 2) = \\frac{6!}{(6-2)!} = \\frac{6!}{4!} = \\frac{6 \\times 5 \\times 4 \\times 3 \\times 2 \\times 1}{4 \\times 3 \\times 2 \\times 1} = 6 \\times 5 = 30$.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers can be formed without repetition of digits ? [amp_mcq option1=”6″ option2=”15″ option3=”30″ option4=”40″ correct=”option3″] This question was previously asked in UPSC CAPF – 2024 Download PDFAttempt Online 30 two-digit numbers can be formed without repetition of digits. The … <\/p>\n

Detailed SolutionOut of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1103,1102],"class_list":["post-90978","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1103","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nOut of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers<\/title>\n<meta name=\"description\" content=\"30 two-digit numbers can be formed without repetition of digits. The given digits are 1, 2, 3, 4, 5, and 6. There are a total of 6 distinct digits. We need to form two-digit numbers without repetition. A two-digit number has a tens digit and a units digit. For the tens digit, we can choose any of the 6 available digits. So, there are 6 choices for the tens digit. Since repetition of digits is not allowed, the units digit must be different from the digit chosen for the tens place. After choosing one digit for the tens place, there are 5 digits remaining. So, there are 5 choices for the units digit. The total number of two-digit numbers that can be formed is the product of the number of choices for each position: Total number of numbers = (Number of choices for tens digit) $times$ (Number of choices for units digit) Total number = $6 times 5 = 30$.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers\" \/>\n<meta property=\"og:description\" content=\"30 two-digit numbers can be formed without repetition of digits. The given digits are 1, 2, 3, 4, 5, and 6. There are a total of 6 distinct digits. We need to form two-digit numbers without repetition. A two-digit number has a tens digit and a units digit. For the tens digit, we can choose any of the 6 available digits. So, there are 6 choices for the tens digit. Since repetition of digits is not allowed, the units digit must be different from the digit chosen for the tens place. After choosing one digit for the tens place, there are 5 digits remaining. So, there are 5 choices for the units digit. The total number of two-digit numbers that can be formed is the product of the number of choices for each position: Total number of numbers = (Number of choices for tens digit) $times$ (Number of choices for units digit) Total number = $6 times 5 = 30$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:42:24+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers","description":"30 two-digit numbers can be formed without repetition of digits. The given digits are 1, 2, 3, 4, 5, and 6. There are a total of 6 distinct digits. We need to form two-digit numbers without repetition. A two-digit number has a tens digit and a units digit. For the tens digit, we can choose any of the 6 available digits. So, there are 6 choices for the tens digit. Since repetition of digits is not allowed, the units digit must be different from the digit chosen for the tens place. After choosing one digit for the tens place, there are 5 digits remaining. So, there are 5 choices for the units digit. The total number of two-digit numbers that can be formed is the product of the number of choices for each position: Total number of numbers = (Number of choices for tens digit) $times$ (Number of choices for units digit) Total number = $6 times 5 = 30$.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/","og_locale":"en_US","og_type":"article","og_title":"Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers","og_description":"30 two-digit numbers can be formed without repetition of digits. The given digits are 1, 2, 3, 4, 5, and 6. There are a total of 6 distinct digits. We need to form two-digit numbers without repetition. A two-digit number has a tens digit and a units digit. For the tens digit, we can choose any of the 6 available digits. So, there are 6 choices for the tens digit. Since repetition of digits is not allowed, the units digit must be different from the digit chosen for the tens place. After choosing one digit for the tens place, there are 5 digits remaining. So, there are 5 choices for the units digit. The total number of two-digit numbers that can be formed is the product of the number of choices for each position: Total number of numbers = (Number of choices for tens digit) $times$ (Number of choices for units digit) Total number = $6 times 5 = 30$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:42:24+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/","url":"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/","name":"Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:42:24+00:00","dateModified":"2025-06-01T10:42:24+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"30 two-digit numbers can be formed without repetition of digits. The given digits are 1, 2, 3, 4, 5, and 6. There are a total of 6 distinct digits. We need to form two-digit numbers without repetition. A two-digit number has a tens digit and a units digit. For the tens digit, we can choose any of the 6 available digits. So, there are 6 choices for the tens digit. Since repetition of digits is not allowed, the units digit must be different from the digit chosen for the tens place. After choosing one digit for the tens place, there are 5 digits remaining. So, there are 5 choices for the units digit. The total number of two-digit numbers that can be formed is the product of the number of choices for each position: Total number of numbers = (Number of choices for tens digit) $\\times$ (Number of choices for units digit) Total number = $6 \\times 5 = 30$.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/out-of-the-six-digits-1-2-3-4-5-and-6-how-many-two-digit-numbers\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"Out of the six digits 1, 2, 3, 4, 5 and 6; how many two digit numbers"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90978","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90978"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90978\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}