As mojotoad points out, when you need that "pick once" functionality from the array, splice() works wonders.. (in the example below, the @testarray has 1052 elements, so the counter runs out at 1051:)
use strict;
my $counter = 0;
my $randstring;
my @testarray = ( 'a' .. 'z', 'A' .. 'Z', '0' .. '999' );
do { $randstring .= splice(@testarray, int rand @testarray, 1);
++$counter;
} until $counter == 1051;
print "$randstring\n";
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