> 
> Each of the letters in the word "MATHEMATICS" is on a letter tile in a
>  bag. Foool picks three without replacement. what is the probability
>  that he will get all vowels?
> 
> 
> 

My approach, 

The number of ways to the letters of the words "MATHEMATICS" can be arranged 3 at a time is coefficient of $x^3 $ $$ 3! \times (1+x)^5 \times \left(1+x+\frac{x^2}{2}\right)^3$$ which is $399$

The number of arrangements of 2A's, 1I and 1E taken 3 at at a time is coefficient of $x^3$ in $$ 3! \times (1+x)^2 \times \left(1+x+\frac{x^2}{2}\right)$$ which is $12$.

Then the required probability is given by $\frac {12}{399} $ but apparently this is not the right answer. What exactly I am missing here?