Permutation of word Question:
Find the permutation of letters of the word EXERCISES in which vowels are together.
My Efforts:
I have rearranged the word in such a way that all the vowel come together.
EEEI XRCSS
Now the vowels can be arranged in $\frac{4!}{3!}$(E is repeated 3 times) ways and remaining letters can be arranged in $\frac{4!}{2!}$(S is repeated 2 times) ways.
Further above shown arrangement can be permuted in $2!$ ways(Consonant can be written first and then vowel.)
So total permutation possible $$\frac{4!}{3!} \times \frac{4!}{2!} \times 2! = 96 $$
But the answer given is $1440$  is is far more than mine, I am surely missing something. 

There are two mistakes I believe.
First of all, there are $5$ remaining letters so there can be $\dfrac{5!}{2!}$ arrangements, and not $\dfrac{4!}{2!}$.
Secondly, the vowels need to be together, not the other letters. For example, S EEEI XRCS is legit. There can be $0, 1, 2, 3, 4$ or $5$ letters before the vowels, so you need to multiply the final result by $6$, not $2$.
The final calculation gives $\dfrac{4!}{3!} \times \dfrac{5!}{2!} \times 6 = 1440$.
