Short Answer TypeHow many 4-digit numbers are there if no digit is repeated?
Or
How many numbers are there between 1000 and 9999 so that no digit is repeated?
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?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that no two consonants are together.
Number of letters = (all distinct)
Number of vowels = 5 (e, i, o, u, a)
Number of consonants = 3 (q, t, n)
Arrange the vowels in a row by leaving one place between every two vowels.
Number of permutations of arrranging vowels ![<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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...(i)
V 
V 
V 
V 
V 
1 2 3 4 5 6
Number of places for the consonants, so that no two of them are together = 6
Number of consonants = 3
n = 6, r = 3
Number of permutations of arranging consonants:
...(ii)
Hence, using (i) and (ii), the number of words formed so that no two consonants are together, using fundamental principle of counting
= 120 x 120 = 14400
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