Question

What is the number of permutations of the word 'QUADRATIC' such that no two vowels and no two
consonants are together?​

Answer 1

1440  number of permutations of the word 'QUADRATIC' such that no two vowels and no two  consonants are together

Step-by-step explanation:

QUADRATIC

Total  - 9

Consonants 5  -  Q  D   R  T  C    

Vowels  4  -  U  A   A   I     ( A Repeated twice)

no two vowels and no two  consonants are together

=> 1  , 3 , 5 , 7  ,  9  Positions by  Consonants in

5! ways

= 120

2 , 4  , 6 ,  8  Positions by Vowels in

4!/2!

= 12  

Total Permutation = 120 * 12

= 1440

1440  number of permutations of the word 'QUADRATIC' such that no two vowels and no two  consonants are together

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