Number of nine-lettered word that can be formed using all the letters of the word 'MEENANSHU' if alike letters are never adjacent is

Options

A. `12xx6!`
B. `11*7!`
C. `13*6!`
D. `12*11*6!`

Answer

B

Explanation

`(b)` `'MEENASHU'` . Number of letters `=9("EE"=2,"NN"=2)`
`:. "Number of ways" =("Total words formed")-("words in which EE together"+"words in which NN together"-"words in which EE together and NN together")`
`=(9!)/(2!*2!)-[(2*8!)/(2!)-7!]`
`=18*7!-7*7!=(18-7)7!=11*7!`