Random distribution of boys and girls into groups c#

Similar questions have been asked before, but not answered the way I can work with it.

I have groups of 3, 4, 5 and 6 and each group is supposed to be filled with 50% boys and 50% girls. The user determines the amount of each group as well as the number of boys and girls.
For instance: 12 girls, 15 boys, 1*3, 2*4, 2*5 and 1*6 groups.

I already got the Random. How I can now put the randomly chosen boys/girls equally into the groups?

Random for boys and group of 4:

for (int i = 0; i < tischgruppenVierer; i++) //for each group of 4
        {

            for (int j = 0; j < 4/2; j++) //only do this two times because 50% boys
            {
                var picked = namesBoys[random.Next(0, namesBoys.Count())]; 
                namesBoys.Remove(picked); //no duplicates
                picked = new TischVier().student;

            }
        }

and the class TischVier:

public class TischVier
    {
        public string student;
    }

I hope this is enough code for you because I hardcoded it for every group.
I appreciate every thought because I am close to despair.