recursive team combinations

[lovekeiiiy]

I need some help. Have an homework assignment where you're suppose to print all possible combinations of a teams of a given size that can be formed group of another size. The assignment is done in a console application.

I understand the gist of the problem. I don't really understand the mathematical formula given in the book: (n, k) = (n ? 1, k ? 1) + (n ? 1, k) k=size of team, n=size of group. I do get overall what it's doing. I found algorithm for the formula that works and finds the number of combinations.

What I was trying to do is create use a list of integers to represent the members of the group. Then have recursive method find the combinations for print the teams. I can't figure out how to print the teams.

recursive method

 //finds and displays all possible teams from given group size, and team size        public static void showTeams(int groupSize, int teamSize, string team)
        {
            //alogrith help/guide from:  https://www.gidforums.com/t-26253.html
            //(n, k) = (n ? 1, k ? 1) + (n ? 1, k) k=size of team, n=size of group (forumal from class textbook)

            //local variables
            
            //base case:  team size is 0
            if(teamSize == 0)
            {
                //team += groupMembers[groupSize].ToString() + " ";
                //Console.WriteLine("team = " + team);
                intTeamCounter++;
                return;
            }
            //base case two:  team size is larger than group size
            else if (groupSize < teamSize)
            {
                //can't have team larger than group.
                return;
            }
            else
            {
               // team += groupMembers[groupSize - 1].ToString() + " ";


                //reduce group size by one, and team size by one
                showTeams(groupSize-1,teamSize-1, team);
                
                showTeams(groupSize-1, teamSize, team);
                
            }
        }

main method

...[code removed]...
//create group list            groupMembers = new int[intSizeOfGroup];
            for(int x = 0; x < intSizeOfGroup; x++)
            {
                groupMembers[x] = (x + 1);
            }

            string team= "";
            //find all team combines and display
            showTeams(intSizeOfGroup, intSizeOfTeam, team);


            //display number of teams found
            Console.WriteLine("The number of team combinations is " + intTeamCounter);

the other code in main is getting team and group size from the user and call methods to validate user input.