Permutations And Combinations

Question
CBSEENMA11014201

How many words, with or without meaning each of 3 vowels and 2 consonants can be formed from the letters of the word ‘INVOLUTE’?

Solution

The word is 'INVOLUTE'
               Number of consonants = 4
                     Number of vowels = 4.
The words formed should contain 3 vowels and 2 consonants.
The problems becomes:
(i)                 Select 3 vowels out of 4.
rightwards double arrow                   Number of selections =space space straight C presuperscript 4 subscript 3
(ii)         Select two consonants out of 4.
rightwards double arrow                    Number of selections = straight C presuperscript 4 subscript 2.
(iii)  Arrange the five letters (3 vowels + 2 consonants) to form words.
                        Number of permutations = 5!
(iv)  Apply fundamental principle of counting:
                 Number of words formed = <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)
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#6 {main}</pre>
                                                  = space space 4 over 1 cross times fraction numerator 4 cross times 3 over denominator 2 cross times 1 end fraction cross times 5 cross times 4 cross times 3 cross times 2 cross times 1
                                                  = 4 x 6 x 120 = 2880  
Hence, the number of words formed  = 2880

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