Question
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
Solution
Number of consonants = 21
Number of vowels = 5
A word contains two vowels and two consonants will be formed as
(i) select 2 vowels out of 5
(ii) select 2 consonants out of 21
(iii) arrange 2 + 2 = 4 letters to obtain different words
(iv) use fundamental principle of counting.
(i) Number of ways in which 2 vowels can be selected out of 5 = 
(ii) Number of ways in which 2 consonants can be selected out of 21 = ![<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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(iii) Number of permutations (to form different words) of the four letters = 4!
Hence, by fundamental principle of counting, the number of words formed.
= 10 x 210 x 24 = 50400
