Given the following language:

$\{$ w in $\{$a$,$ b$,$ c$\}*|$ w has as many a$,$ b$,$ and c$,$ modulo $2\}.$ That is$,$ the parities $($odd$/$even$)$ of a$,$ b$,$ and c are the same.

over the alphabet $\{$ a b c $\}$

Do you believe that the language is regular?