gistfile1.txt

#!/usr/bin/perl

use strict;
use warnings;
use Data::Dumper;
use List::Util qw/shuffle/;

my $roop    = 1000;
my $number  =  100;
my $limit   =   50;
my @persons = 1 .. $number;
my $success = 0;

foreach ( 1 .. $roop ) {
    my $cards = [ shuffle 1 .. $number ];
    $success++ if ( is_success($cards) );
}

print $success / $roop, "\n";

sub is_success {
    my $cards = shift;
    my $is_ok = 0;
  PERSON: foreach my $num (@persons) {
        my $my_num = $num;
      CARD: foreach ( 1 .. $limit ) {
            $num = $cards->[ $num - 1 ];
            next CARD unless ( $my_num eq $num );
            $is_ok++;
            next PERSON;
        }
    }
    return ( $is_ok eq $number ) ? 1 : 0;
}