The five vowels $A$, $E$, $I$, $O$ and $U$ along with$15$ $X$'s are to be arranged in a row such that no $X$ is at an extreme position. Also, between any two vowels there must be at least $3$ $X$'s. Find the number of ways in which this can be done.
I have tried but failed to get the correct answer. Please help me to give any reference to solve it.
Thanks in advance.