Permutations And Combinations

Question
CBSEENMA11014110

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?

Solution

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.
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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
 

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