Permutations And Combinations


How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?


Number of letters = (all distinct)
Number of vowels = 5 (e, i, o, u, a)
Number of consonants = 3 (q, t, n)
Step I:   Tie the vowels together
rightwards double arrow        Number of permutations = straight P presuperscript 5 subscript 5 equals space 5 factorial space equals space 120
Step II:   Tie the consonants together.
rightwards double arrow         Number of permutations = <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/ at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/ line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
#1 /home/config_admin/public/ mkdir('/home/config_ad...', 493)
#2 /home/config_admin/public/ com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/ com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/ com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/ com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>
Step III:  Mix the bundles and any remaining letter to give 1 + 1 + 0 = 2 letters.
             Number of permutations = space space straight P presuperscript 2 subscript 2 equals 2 factorial comma space equals space 2
             Hence, the number of permutations, using, fundamental principle of counting 
                                                 = 120 x 6 x 2 = 1440

Sponsor Area

Some More Questions From Permutations and Combinations Chapter