The letters of the word CASTIGATION is arranged in different ways randomly. What is the chance that vowels occupy the even places ?

 Vowels are A I A I O, 

 C    A   S    T   I    G   A    T   I    O   N

(O) (E) (O) (E) (O) (E) (O) (E) (O) (E) (O)

So there are 5 even places in which five vowels can be arranged and in rest of 6 places 6 constants can be arranged as follows :

$n\left(E\right)=\frac{5P5}{2!*2!(A,I are 2 times)}*\frac{6P6}{2!(T is 2 times)}=21600$

$n\left(S\right)=\frac{11!}{2!*2!*2!(A, I are 2 times)}=4989600$

$\frac{21600}{4989600}=0.043$