Without LINQ, you can use a nested loop:
var permutations = new List();
for(int i = 0; i < myString.Count; i++)
{
for(int j = 0; j < myString.Count; j++)
{
if(i == j)
continue;
var permutation = string.Format("{0}{1}", myString[i], myString[j]);
permutations.Add(permutation);
}
}