Doubt in permutation

Question

what is number of permutation of NADEEAKY

Edit : I forgot to add condition : all vowel should not be together

is it 9360 or 10050

Comments

$\frac{ 8! }{2! \times 2!}$

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is it correct ? I don't think so.

 

We need to group (A,E,E,A)

 

So , we need to subtract from the total permutations

 

(8! /(2! * 2!)) - (5!)*(4!/2!*2!)

 

 

Please correct me if I am wrong.

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you are right and ans. is 9360.

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thanks everyone for answers