#!/usr/bin/perl
use warnings;
use strict;
use 5.010; # defined-or, say

my @tiles = (('_') x 2,  # 2 blank tiles (scoring 0 points)
             # 1 point
             ('E') x 12,
             qw(A I) x 9,
             ('O') x 8,
             qw(N R T) x 6,
             qw(L S U) x 4,
             # 2 points
             ('D') x 4,
             ('G') x 3,
             # 3 points
             qw(B C M P) x 2,
             # 4 points
             qw(F H V W Y) x 2,
             # 5 points
             ('K'),
             # 8 points
             qw(J X),
             # 10 points
             qw(Q Z));

my $rack_size = 5;

my %hash;
my @rack = 0 .. $rack_size - 1;
while ($rack[-1] != @tiles) {
    my $string = join q(), map $tiles[$_], @rack;
    $hash{$string}++;
    my $first_to_move = 0;
    $first_to_move++ while $rack[$first_to_move] + 1 == ($rack[$first_to_move + 1] // -1);
    $rack[$first_to_move]++;
    for my $i (0 .. $first_to_move - 1) {
        $rack[$i] = $i;
    }
}

my $combinations = keys %hash;

my $sum = 0;
$sum += $_ for values %hash;

print map "$_ => " . ($hash{$_} / $sum) . "\n", sort { $hash{$a} <=> $hash{$b} } keys %hash;
print "Combinations: $combinations, Count: $sum.\n";