With a problem like this where you know the 3 possibilities, tr is usually the way to go for speed. Splitting and making hashes and such will usually be slower than 3 very fast trips through the string.
"save me a number of lines" would normally be the last thing I would be thinking about, ranking way below: clarity, speed, memory usage. Its hard to argue with clearly written fast code.
#!/usr/bin/perl -w
use strict;
my $string="CCCAAAAACCCAAAAAAACCCCBBBCCAAACCBBACBBAAAAAAAAAAACAAAAAAAA
+AA";
my $nA = $string =~ tr/A//;
my $nB = $string =~ tr/B//;
my $nC = $string =~ tr/C//;
print "A=$nA B=$nB C=$nC"; #A=37 B=7 C=16
#compare these 3 as you will to handle cases like
#all are the same, etc
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