Question

in how many ways can the letters of the word NINETEEN be arranged so that niether all the vowels nor all the consonants are together
​

Answer 1

Given, word NINETEEN

No 3 E's should come together hence E's can be arranged in  

3!

6

P  

3

​  

 

​  

 ways.

And the remaining 5 letters can be arranged is 5! ways and as N is repeating trice divide by 3! ways  

∴ the total number of ways are  

3!

5!

​  

 

3!

6

P  

3

​  

 

​  

 ways

=  

3!

5!

​  

×  

6

C  

3

​  

 ways