use strict;
use warnings;

sub nCr {
    my ($n, $r) = @_;
    my $res = 1;
    for my $i (1..$r) {
        $res *= $n--;
        $res /= $i;
    }
    $res;
}

my %bag = (
    "\@" => 2,  # blank
    'A' => 9,
    'B' => 2,
    'C' => 2,
    'D' => 4,
    'E' => 12,
    'F' => 2,
    'G' => 3,
    'H' => 2,
    'I' => 9,
    'J' => 1,
    'K' => 1,
    'L' => 4,
    'M' => 2,
    'N' => 6,
    'O' => 8,
    'P' => 2,
    'Q' => 1,
    'R' => 6,
    'S' => 4,
    'T' => 6,
    'U' => 4,
    'V' => 2,
    'W' => 2,
    'X' => 1,
    'Y' => 2,
    'Z' => 1,
);

my $compute_prob = 1;
my $racksize = 7;

my $total_number_of_tiles;
foreach my $char (keys %bag) {
    $total_number_of_tiles += $bag{$char};
}
my @letters = sort keys %bag;

my %pos;
foreach my $i (0 .. $#letters) {
    $pos{$letters[$i]} = $i;
}

my $all_combinations = nCr($total_number_of_tiles, $racksize);
my %counter = (1 => '', 2 => '',3 => '',4 => '',5 => '',6 => '',7 => '
+',);

foreach my $s1 (@letters) {
    %counter = ($s1 => 1);
    foreach my $s2 (@letters[$pos{$s1}..$#letters])  {
        $counter{$s2}++;
        if ($counter{$s2} > $bag{$s2}) {
            $counter{$s2}--;
            next;
        }
        foreach my $s3 (@letters[$pos{$s2}..$#letters])  {
            $counter{$s3}++;
            if ($counter{$s3} > $bag{$s3}) {
                $counter{$s3}--;
                next;
            }
            foreach my $s4 (@letters[$pos{$s3}..$#letters])  {
                $counter{$s4}++;
                if ($counter{$s4} > $bag{$s4}) {
                    $counter{$s4}--;
                    next;
                }
                foreach my $s5 (@letters[$pos{$s4}..$#letters])  {
                    $counter{$s5}++;
                    if ($counter{$s5} > $bag{$s5}) {
                        $counter{$s5}--;
                        next;
                    }
                    foreach my $s6 (@letters[$pos{$s5}..$#letters])  {
                        $counter{$s6}++;
                        if ($counter{$s6} > $bag{$s6}) {
                            $counter{$s6}--;
                            next;
                        }
                        foreach my $s7 (@letters[$pos{$s6}..$#letters]
+)  {
                            $counter{$s7}++;
                            if ($counter{$s7} > $bag{$s7}) {
                                $counter{$s7}--;
                                next;
                            }
                            my $rack = join '', $s1,$s2,$s3,$s4,$s5,$s
+6,$s7;
                            
                            if ($compute_prob) {
                                my $thiscombo = 1;
                                foreach my $c (keys %counter) {
                                    my $in_bag = $bag{$c};
                                    my $in_rack = $counter{$c};
                                    my $res = nCr($in_bag, $in_rack);
                                    $thiscombo *= $res;
                                }
                                my $probability = sprintf("%.5g", $thi
+scombo/$all_combinations);
                                print "$rack $probability\n";
                            }
                            else {
                                print "$rack\n";
                            }
                            $counter{$s7}--;
                        }
                        $counter{$s6}--;
                    }
                    $counter{$s5}--;
                }
                $counter{$s4}--;
            }
            $counter{$s3}--;
        }
        $counter{$s2}--;
    }
    $counter{$s1}--;
}

__END__
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