Exercise 10

Let $X$ 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 elsewhere in the string).

• Precisely four of the symbols in the string are the letter '$t$'.

• Precisely three characters in the string are elements of the set $V=\{a,e,i,o,u\}$ and these characters are all distinct.