Cartesian product of multiple combinations memory issue

Question

Yo,

Im running into a small issue. I have a selection of "Players" I am trying to run some probability predictions on. There is 112 players. Of these players the following is true:

• 64 can bat.
• 66 can bowl.
• 10 can be wicket keepers
• Any player can be able to do up too any two of bowl/bat/wicket keep but at least one.

A Team is made up of:

• 7 players that can bat.
• 7 players that can bowl.
• 2 players that can wicket keepers.
• There cannot be duplicate players in a team.
• A player may only fulfill one role even if they are capable of two.( a batter / bowler must bat or bowl not both)

Now to the problem

I Have the following code.

var allBattingCombos = new Combinations<int>(players.Where(player => player.inRoundCanBat).Select(player => player.fantasyID).ToList(), 7);
var allBowlingCombos = new Combinations<int>(players.Where(player => player.inRoundCanBowl).Select(player => player.fantasyID).ToList(), 7);
var allWKTCombos = new Combinations<int>(players.Where(player => player.inRoundCanWkt).Select(player => player.fantasyID).ToList(), 2);

var allCombos = new List<Combinations<int>>() { allBowlingCombos , allBowlingCombos, allWKTCombos };
var allTeamCombos = allCombos.CartesianProduct().ToList();

Where CartesianProduct(from Finding all combinations from sets of possibilities) =

public static IEnumerable<IEnumerable<T>> CartesianProduct<T>(this IEnumerable<IEnumerable<T>> sequences)
{
    // Default object
    IEnumerable<IEnumerable<T>> emptyProduct = new[] { Enumerable.Empty<T>() };

    return sequences.Aggregate(
        emptyProduct,
        (accumulator, sequence) =>
        from accseq in accumulator
        from item in sequence
        select accseq.Concat(new[] { item }));
}

I get the following values:

allBattingCombos count = 621216192
allBowlingCombos count = 778789440
allWKTCombos count = 45

All team combos locks my pc and eventually it dies as I run out of memory. While I was waiting for my calculation to run I did some maths. According to Memory size of a list of int 4 bytes min per int in the list so thats:

4 bytes * 
15 member ids in a team * 
621216192 batting combos * 
778789440 bowling combos *
45 wkt combos

= 1.34E+21 bytes

or 13400000000000 gigaBytes

Yikes, ain't nobody got ram like dat.

What makes it more scary is I need to run it 9 times, 1 for each round.

Once I have my team possibilities I need to run something like this on each team.

Team highestScoringTeam = null;

foreach (var team in allTeamCombos)
{
    var teamobj = new Team();
    teamobj.BattersList = team[0].ToList();
    teamobj.BowlersList = team[1].ToList();
    teamobj.WktKeepersList = team[2].ToList();
    if (highestScoringTeam == null)
    {
        highestScoringTeam = teamobj;
    }
    else if (teamobj.TeamIsValid && teamobj.TotalScoreForRound > highestScoringTeam.TotalScoreForRound)
    {
        highestScoringTeam = teamobj;
    }
}

Does anyone know how I can get around my ram issue / see a better way of achieving my goals?

----Update 1----

After some thinking I don't need the whole list object at any point I can just use it during the Cartesian calculation. In place of allTeamCombos I use the following.

foreach (var battingCombo in allBattingCombos)
{
    foreach (var bowlingCombo in allBowlingCombos)
    {
        foreach (var WktCombo in allWKTCombos)
        {
            var team = new Team();

            team.BattersList = battingCombo.Select(id => players.First(p => p.fantasyID == id)).ToList();
            team.BowlersList = bowlingCombo.Select(id => players.First(p => p.fantasyID == id)).ToList();
            team.WktKeepersList = WktCombo.Select(id => players.First(p => p.fantasyID == id)).ToList();
            if (highestScoringTeam == null)
            {
                highestScoringTeam = team;
            }
            else if (team.TeamIsValid && team.TotalScoreForRound > highestScoringTeam.TotalScoreForRound)
            {
                highestScoringTeam = team;
                Console.WriteLine("new highScore = " + team.TotalScoreForRound);
            }

            combinationsParsed++;
            if(combinationsParsed % 10000 == 0)
                Console.WriteLine("combinationsParsed = " + combinationsParsed);
        }
    }

I'm thinking that this solves the question of the ram issue, I'm also thinking I should maybe close the question.