C# - picking different combinations out of a list of elements

var list = new List<int> { 1, 2, 3, 4, 5, 6 };
var allCombinations = list.Permute().ToList();
var stringList = new List<string>();

foreach (var item in allCombinations)
{
      stringList.Add(string.Join(",", item.Select(n => n.ToString()).ToArray()));
}

public static class Extensions
{
	public static IEnumerable<IEnumerable<T>> Permute<T>(this IEnumerable<T> sequence)
	{
		if (sequence == null)
		{
			yield break;
		}

		var list = sequence.ToList();

		if (!list.Any())
		{
			yield return Enumerable.Empty<T>();
		}
		else
		{
			var startingElementIndex = 0;
			foreach (var startingElement in list)
		    {
				var remainingItems = list.Where((e, i) => i != startingElementIndex);

				foreach (var permutationOfRemainder in remainingItems.Permute())
				{
					yield return startingElement.Concat(permutationOfRemainder);
				}

				startingElementIndex++;
			}
		}
	}

	private static IEnumerable<T> Concat<T>(this T firstElement, IEnumerable<T> secondSequence)
	{
		yield return firstElement;
		if (secondSequence == null)
		{
			yield break;
		}

		foreach (var item in secondSequence)
		{
			yield return item;
		}
	}
}

Quote:

I'm stuck on the logic.