Without putting all the filenames into memory:

opendir DIR, "somedirectory" or die "opendir: $!\n";
my $count;
!/\A\.\.?\z/ && $count++ while defined($_ = readdir(DIR));
closedir DIR or warn "closedir: $!\n";
print "$count\n";
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(You'd need to add a -f or similar test for it to only consider plain files, or non-directories, etc.)