Beatnik nailed it, but he left out the numerals 2 through 9 and added an extra parenthesis to the second line. The exact solution is thus:

use strict;
my @chars = ("a".."z","A".."Z", 2..9);
my $random_string = join("",@chars[map{ rand @chars} (1..8)]); 
#8 being the number of chars to randomize ofcourse
print "$random_string\n";
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