Maybe this solution - however it does not rely on file2 to calculate the combinations. That is done instead using Algorithm::Combinatorics.

#!/usr/bin/perl
use strict;
use warnings;
use Algorithm::Combinatorics 'subsets';

my @headers = split ' ', scalar <DATA>;
my @data = map [split], <DATA>;

my @subsets;
for my $k (3, 4) {
    push @subsets, subsets([0 .. $#headers], $k);
}

for my $indices (@subsets) {
    my $count = 0;
    for my $aref (@data) {
        ++$count unless grep $_ eq '0', @$aref[ @$indices ];
    }
    print "@headers[ @$indices ]\t$count\n";    
}

__DATA__
A    B    C    D    E
0    0    0    +    0
+    0    +    +    +
0    +    +    +    +
0    0    +    +    0
+    +    +    +    +
0    +    +    +    +
+    0    +    +    0
[download]

The output is

A B C   1
A B D   1
A B E   1
A C D   3
A C E   2
A D E   2
B C D   3
B C E   3
B D E   3
C D E   4
A B C D 1
A B C E 1
A B D E 1
A C D E 2
B C D E 3
[download]