Find the number of way in which the letters of the word 'EXTENSION' can be arranged in a straight line so that no two vowels are next to each other?
This is how i did it:
_X_T_N_S_N_
'_' symbols indicate where the vowels could possibly go
$${_6}C_4 \cdot \dfrac{4!}{2!} \cdot \dfrac{5!}{2!} = 10800$$
However, the answer book says that the answer is 60 so i don't know what i'm doing wrong