Generating all the combinations then filtering out the unneeded ones could take a lot lot lot longer than necessary. This is what the earlier solutions do. However, the following program avoids generating extra combinations. 

use strict;
use warnings;
use feature qw( say );

use Algorithm::Loops    qw( NestedLoops );
use Math::Combinatorics qw( combine );
use Sort::Key           qw( rukeysort );     # Optional.

my @strings = qw( a?1 a?2 a%3 b?2 b?3 b%5 c%4 c%5 c?6 d%2 );
my @mandatory_types = qw( a? b% c? );
my $n = 4;

$n -= @mandatory_types;

# ( [ "a?1", "a?", 1 ], ... )
my @split_strings =
   map { [ /^((.+)(\d+))\z/a ] }
      @strings;

my %by_weight;
for ( @split_strings ) {
   push @{ $by_weight{ $_->[2] } }, $_;
}

my @mandatory_lists =
   map {
      my $type = $_;
      [
         grep { $_->[1] eq $type }
            @split_strings
      ]
   }
      @mandatory_types;

my @loops;
for my $list ( @mandatory_lists ) {
   push @loops, sub {
      my %seen_weights =
         map { $_->[2] => 1 }
            @_;

      return [
         grep { !$seen_weights{ $_->[2] } }
            @$list
      ];
   };
}

my $mandatory_iter = NestedLoops( \@loops );
while ( my @mandatory_picks = $mandatory_iter->() ) {
   my %seen_weights =
      map { $_->[2] => 1 }
         @mandatory_picks;

   my @buckets =
      map { $by_weight{ $_ } }
         grep { !$seen_weights{ $_ } }
            keys( %by_weight );

   my $bucket_iter = Math::Combinatorics->new(
      count => $n,
      data  => \@buckets,
   );

   while ( my @bucket_picks = $bucket_iter->next_combination() ) {
      my $other_iter = NestedLoops( \@bucket_picks );
      while ( my @other_picks = $other_iter->() ) {
         say
           join ",",
              map { $_->[0] }
                 rukeysort { $_->[2] }
                    @mandatory_picks, @other_picks;
      }
   }
}

[download]
c?6,b%5,a?2,a?1
c?6,b%5,b?2,a?1
c?6,b%5,d%2,a?1
c?6,b%5,a%3,a?1
c?6,b%5,b?3,a?1
c?6,b%5,c%4,a?1
c?6,b%5,a%3,a?2
c?6,b%5,b?3,a?2
c?6,b%5,c%4,a?2
c?6,b%5,a?2,a?1

[download]

More interesting test: 

my @strings = qw( a?1 a?2 a%3 b?2 b?3 b%5 c%4 c%5 c?6 d%2 a?7 c?7 );
my @mandatory_types = qw( a? b% c? );                   # ^^^^^^^
my $n = 5;
#       ^

[download]
a?7,c?6,b%5,a%3,a?1
a?7,c?6,b%5,b?3,a?1
c?7,c?6,b%5,a%3,a?1
c?7,c?6,b%5,b?3,a?1
a?7,c?6,b%5,a?2,a?1
a?7,c?6,b%5,b?2,a?1
a?7,c?6,b%5,d%2,a?1
c?7,c?6,b%5,a?2,a?1
c?7,c?6,b%5,b?2,a?1
c?7,c?6,b%5,d%2,a?1
a?7,c?6,b%5,c%4,a?1
c?7,c?6,b%5,c%4,a?1
c?6,b%5,a%3,a?2,a?1
c?6,b%5,a%3,b?2,a?1
c?6,b%5,a%3,d%2,a?1
c?6,b%5,b?3,a?2,a?1
c?6,b%5,b?3,b?2,a?1
c?6,b%5,b?3,d%2,a?1
c?6,b%5,c%4,a%3,a?1
c?6,b%5,c%4,b?3,a?1
c?6,b%5,c%4,a?2,a?1
c?6,b%5,c%4,b?2,a?1
c?6,b%5,c%4,d%2,a?1
c?7,c?6,b%5,c%4,a?1
c?7,b%5,c%4,a%3,a?1
c?7,b%5,c%4,b?3,a?1
c?7,b%5,c%4,a?2,a?1
c?7,b%5,c%4,b?2,a?1
c?7,b%5,c%4,d%2,a?1
c?7,c?6,b%5,a%3,a?1
c?7,c?6,b%5,b?3,a?1
c?7,c?6,b%5,a?2,a?1
c?7,c?6,b%5,b?2,a?1
c?7,c?6,b%5,d%2,a?1
c?7,b%5,a%3,a?2,a?1
c?7,b%5,a%3,b?2,a?1
c?7,b%5,a%3,d%2,a?1
c?7,b%5,b?3,a?2,a?1
c?7,b%5,b?3,b?2,a?1
c?7,b%5,b?3,d%2,a?1
c?6,b%5,c%4,a?2,a?1
a?7,c?6,b%5,c%4,a?2
c?7,c?6,b%5,c%4,a?2
c?6,b%5,c%4,a%3,a?2
c?6,b%5,c%4,b?3,a?2
a?7,c?6,b%5,a?2,a?1
c?7,c?6,b%5,a?2,a?1
c?6,b%5,a%3,a?2,a?1
c?6,b%5,b?3,a?2,a?1
a?7,c?6,b%5,a%3,a?2
a?7,c?6,b%5,b?3,a?2
c?7,c?6,b%5,a%3,a?2
c?7,c?6,b%5,b?3,a?2
c?7,b%5,a%3,a?2,a?1
c?7,b%5,b?3,a?2,a?1
c?7,b%5,c%4,a?2,a?1
c?7,c?6,b%5,a?2,a?1
c?7,b%5,c%4,a%3,a?2
c?7,b%5,c%4,b?3,a?2
c?7,c?6,b%5,a%3,a?2
c?7,c?6,b%5,b?3,a?2
c?7,c?6,b%5,c%4,a?2
a?7,c?6,b%5,c%4,a?2
a?7,c?6,b%5,c%4,b?2
a?7,c?6,b%5,c%4,d%2
a?7,c?6,b%5,a%3,a?2
a?7,c?6,b%5,b?3,a?2
a?7,c?6,b%5,a%3,b?2
a?7,c?6,b%5,b?3,b?2
a?7,c?6,b%5,a%3,d%2
a?7,c?6,b%5,b?3,d%2
a?7,c?6,b%5,a?2,a?1
a?7,c?6,b%5,b?2,a?1
a?7,c?6,b%5,d%2,a?1
a?7,c?6,b%5,c%4,a%3
a?7,c?6,b%5,c%4,b?3
a?7,c?6,b%5,c%4,a?1
a?7,c?6,b%5,a%3,a?1
a?7,c?6,b%5,b?3,a?1

[download]

In reply to Re: Combinations with constraints by ikegami
in thread Combinations with constraints by Anonymous Monk

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