{"id":6022,"date":"2021-10-04T22:59:46","date_gmt":"2021-10-04T17:29:46","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6022"},"modified":"2021-10-04T23:00:27","modified_gmt":"2021-10-04T17:30:27","slug":"permutation-combination-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/permutation-combination-examples\/","title":{"rendered":"Permutation and Combination Examples"},"content":{"rendered":"

Here you will learn some permutation and combination examples for better understanding of permutation and combination concepts<\/a>.<\/p>\n\n\n

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Example 1 : <\/span> If all the letters of the word ‘RAPID’ are arranged in all possible manner as they are in a dictionary, then find the rank of the word ‘RAPID’.<\/p>\n

Solution : <\/span>First of all, arrange all letters of given word alphabetically : ‘ADIPR’

\n\t\t\tTotal number of words starting with A _ _ _ _ = 4! = 24

\n\t\t\tTotal number of words starting with D _ _ _ _ = 4! = 24

\n\t\t\tTotal number of words starting with I _ _ _ _ = 4! = 24

\n\t\t\tTotal number of words starting with P _ _ _ _ = 4! = 24

\n\t\t\tTotal number of words starting with R A D _ _ = 2! = 2

\n\t\t\tTotal number of words starting with R A I _ _ = 2! = 2

\n\t\t\tTotal number of words starting with R A P D _ = 1 = 1

\n\t\t\tTotal number of words starting with R A P I _ = 1 = 1

\n\t\t\t\\(\\therefore\\) Rank of the word RAPID = 24 + 24 + 24 + 24 + 2 + 2 + 1 + 1 = 102<\/p>\n


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Example 2 : <\/span> Find the number of ways of dividing 52 cards among 4 players equally such that each gets exactly one Ace.<\/p>\n

Solution : <\/span>Total number of ways of dividing 48 cards(Excluding 4 Aces) in 4 groups = \\(48!\\over (12!)^4 4!\\)

Now, distribute exactly one Ace to each group of 12 cards. Total number of ways = \\(48!\\over (12!)^4 4!\\) \\(\\times\\) 4!

Now, distribute these groups of cards among four players

= \\(48!\\over (12!)^4 4!\\) \\(\\times\\) 4!4! = = \\(48!\\over (12!)^4\\) \\(\\times\\) 4! \n <\/p>


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Example 3 : <\/span> How many numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?<\/p>\n

Solution : <\/span>There are 4 odd digits (1, 1, 3, 3) and 4 odd places(first, third, fifth and seventh). At these places the odd digits can be arranged in \\(4!\\over 2!2!\\) = 6

Then at the remaining 3 places, the remaining three digits(2, 2, 4) can be arranged in \\(3!\\over 2!\\) = 3 ways

\\(\\therefore\\)     The required number of numbers = 6 \\(\\times\\) 3 = 18<\/p>\n


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Example 4 : <\/span> In how many ways can 5 different mangoed, 4 different oranges & 3 different apples be distributed among 3 children such that each gets atleast one mango?<\/p>\n

Solution : <\/span>5 different mangoes can be distributed by following ways among 3 children such that each gets at least 1 :

Total number of ways : (\\(5!\\over 3!1!1!2!\\) + \\(5!\\over 2!2!2!\\)) \\(\\times\\) 3!

Now, the number of ways of distributing remaining fruits (i.e. 4 oranges + 3 apples) among 3 children = \\(3^7\\) (as each fruit has 3 options).

\\(\\therefore\\)     Total number of ways = (\\(5!\\over 3!2!\\) + \\(5!\\over {(2!)}^3\\)) \\(\\times\\) 3! \\(\\times\\) \\(3^7\\)<\/p>\n
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Practice these given permutation and combination examples to test your knowledge on concepts of permutation and combination.<\/p> \n <\/div>\n <\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn some permutation and combination examples for better understanding of permutation and combination concepts. Example 1 : If all the letters of the word ‘RAPID’ are arranged in all possible manner as they are in a dictionary, then find the rank of the word ‘RAPID’. Solution : First of all, arrange all …<\/p>\n

Permutation and Combination Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[18],"tags":[],"yoast_head":"\nPermutation and Combination Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"Solve these Permutation and Combination examples to practice and test your knowledge of Permutation & Combination concepts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/permutation-combination-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Permutation and Combination Examples - 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