Just for variety, a recursive solution suggests itself.

use strict;
use warnings;

sub add_to {
  my ($target, $first_card, @others) = @_;
  # Base cases
  return [$first_card] if $first_card == $target;
  return () if @others == 0;
  # The set of cards adding up to target is
  # the set of cards adding up to target that include first_card, AND
  # the set of cards adding up to target that don't include first_card
  return (map([$first_card, @$_], add_to($target-$first_card, @others)
+)
         , add_to($target, @others));
}

my @hand = map 1+int(rand(10)), 1..7;
print "Hand is @hand\n";
print "@$_\n" for add_to(15, @hand);
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