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Permutations And Combinations

Question
CBSEENMA11014114
Wired Faculty App

In how many ways can 5 girls be seated in a row so that two girls Ridhi and Sanya are:

(a) always together (b) never together

Solution

Number of girls = 5
(a)    Consider Ridhi and Sanya together as one girl.
        Now, number of girls becomes 4
        Number of permutation of arranging these 4 girls = straight P presuperscript 4 subscript 4 space equals space fraction numerator 4 factorial over denominator 0 factorial end fraction space equals space 4 factorial space equals space 24
        But, the two girls Ridhi and Sanya can be arranged in <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre> ways or 2! ways or 2 ways.
        By fundamental principle of counting, the required number of permutations = 24 x 2 = 48
(b)    Total number of permutations = straight P presuperscript 5 subscript 5 space equals space 5 factorial space equals space 120
        Number of permutations in wich Ridhi and Sanya are never together:
                                             = 120 - 48 = 72

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