How about skipping the openning of the external file and just doing something simple like this:
#!/usr/bin/perl -w
use strict;
# Make declarations of variables.
my @alpha = ('a'..'z', 'A'..'Z');
my @numeric = (0 .. 9);
my ($a_pwd0, $a_pwd1, $a_pwd2,
$a_pwd3, $n_pwd0, $n_pwd1);
# Choose random letters and numbers for each string.
$a_pwd0 = $alpha[int rand @alpha];
$a_pwd1 = $alpha[int rand @alpha];
$a_pwd2 = $alpha[int rand @alpha];
$a_pwd3 = $alpha[int rand @alpha];
$n_pwd0 = $numeric[int rand @numeric];
$n_pwd1 = $numeric[int rand @numeric];
# Print password:
print "\n\n", "Your password is: ",
$a_pwd0,$n_pwd0,$n_pwd1,$a_pwd1,
$a_pwd2,$a_pwd3, "\n\n";
exit;