Read names (lines of text) from text file, permute them and write result to another text file.

permutation.cs

using System;
using System.Collections.Generic;
using System.IO;

namespace AssignmentRandomizer
{
    class Program
    {
        static void Main()
        {
            var names = File.ReadAllLines("names.txt");

            var permutation = GetRandomPermutation(names);

            File.WriteAllText("permutation.txt",string.Join('\n',permutation));
        }

        private static IEnumerable<T> GetRandomPermutation<T>(IList<T> names)
        {
            var rnd = new Random();
            names=new List<T>(names);
            for (int i = 0; i < names.Count; i++)
            {
                int choice = i+rnd.Next(names.Count-i);
                Swap(names, i, choice);
            }
            return names;
        }

        private static void Swap<T>(IList<T> items, int i1, int i2)
        {
            var tmp = items[i1];
            items[i1] = items[i2];
            items[i2] = tmp;
        }
    }
}