One way to do it, (using tr).

#!/usr/bin/perl
use strict;
use warnings;

my $s='ABCAAAABBBCCCCCAAABBBCCC';

if (0 == $s =~ tr/ABC//c) {
    print "All letters are A B or C";
}
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Note that I didn't use $a or $b as those should be reserved for the sort function.

Chris