Use an input array to draw your values from:
private static string RandomString(int length)
{
const string pool = "abcdefghijklmnopqrstuvwxyz0123456789";
var builder = new StringBuilder();
for (var i = 0; i < length; i++)
{
var c = pool[random.Next(0, pool.Length)];
builder.Append(c);
}
return builder.ToString();
}
Or the (inevitable) Linq solution:
private static string RandomString(int length)
{
const string pool = "abcdefghijklmnopqrstuvwxyz0123456789";
var chars = Enumerable.Range(0, length)
.Select(x => pool[random.Next(0, pool.Length)]);
return new string(chars.ToArray());
}