Given the string "ENGINEER", how might one find the number of permutations that contain only three consecutive vowels?
Same question for 2 consecutive vowels can be found here. I tried to solve this in the same way as given below.
Arrange the $4$ consonants: $\dfrac{4!}{2!}$
Choose $2$ slots: $\dbinom{5}{2}$
One slot from the above is for the group of $3$ vowels: $\dbinom{2}{1}$
Arrange the $4$ vowels $\dfrac{4!}{3!}$
Their product is coming to $960$
But, actual answer is $1200$ (I tested using a java program).
Please help to understand where I am going wrong.