Palindromic Score

Alice has three types of characters: $A$, $B$ and $C$. She is given exactly $X$ copies of $A$, $Y$ copies of $B$, and $Z$ copies of $C$. Alice must use all these characters to form a string. She is free to arrange the characters in any order of her choosing. After Alice forms her string, Bob makes a move. Bob will choose one character type from { $A$, $B$, $C$ } and delete **all** its occurrences