SHOW ALL YOUR WORKLet $x$ be the set of the $26$ lowercase English letters and $10$ decimal digits. How

many $x-$strings of length $15$ satisfy all of the following properties $($at the same time$)?$

The first and last symbols of the string are distinct digits $($which may appear else$-$

where in the string$).$

Precisely four of the symbols in the string are the letter $\text{'}t\text{'}.$

Precisely three characters in the string are elements of the set $V=\{a,e,i,o,u\}$

and these characters are all distinct.