>>>Haven't figured out the total number of permutations yet
>>>
>>>Say, 6 chars with at least one digit
>>>
>>>I can put the digit in the first position, second, third, ... sixth
>>>
>>>So that would be 6 * 52^5 * 10 which is 52^5 * 60 and this is greater than 52^6
>>
>>Couldn't resist a quick play:

       private static void Main(string[] args)
>>        {
>>            Stopwatch watch = new Stopwatch();
>>            watch.Start();
>>            foreach (string s in GetValidPasswordList())
>>            {
>>                Console.WriteLine(s);
>>            }
>>            Console.WriteLine(watch.Elapsed);
>>            Console.ReadLine();
>>        }
>>
>>        public static IEnumerable<string> GetValidPasswordList()
>>        {
>>            int total = 0;
>>            for (int x = 1; x<63; x++)
>>            {
>>                for (int y = 1; y<63; y++)
>>                {
>>                    for (int z = 0; z < ((y < 53 && x < 53) ? 63 : 11); z++) //24 seconds
>>                    //for (int z = 0; z < 63; z++ ) // 31 seconds
>>                    {
>>                        yield return string.Format("{0}.{1}.{2}  (Total:{3})", x, y, z, total++);
>>                    }
>>                }
>>            }
>>        }

>>Couldn't be bothered with real chars but the principle's the same. 24 seconds v 31
>
>
>(1) Done the same - added two methods ( Possibilities() and ListPossibilities())
>GetValidPasswordList() yields 182,192 possibilities
>
>The others yield 97,720 possibilities
>
>(2) And to answer the question:
>How many possibilties are there for a password of 6 upper/lower case chars where at least one upper and at least one lower
>
>See method Password6()
>
>The answer is 19,152,778,112
>
>this is 96.88% of 52^6
>
>
>But I haven't been able to find a formula
>
>

>delegate IEnumerable<string> TheMethod();
>	public static class AClass
>	{
>
>		static long Total = 0L;
>		static string AlphaDigit = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789";
>		static string Alpha = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
>
>		public static void Main()
>		{
>
>			string s = null;
>
>			TheMethod[] list = { GetValidPasswordList, Possibilities, ListPossibilities };
>
>			foreach (TheMethod method in list)
>			{
>				foreach (string x in method())
>				{
>					s = x;
>				}
>
>				Console.WriteLine("Method {0}   {1}", method.GetInvocationList()[0].Method.Name, s);
>			}
>
>			Console.WriteLine("password 6 with at least one upper and at least one lower {0}", Password6());
>			Console.ReadLine();
>		}
>		static IEnumerable<string> Possibilities()
>		{
>			Total = 0;
>			// 1- 10 is digit
>			// 11 - 62 is a-zA-Z
>
>			for (int i = 1; i < 63; i++)
>				for (int j = 1; j < 63; j++)
>					for (int k = 1; k < 63; k++)
>						if (i > 10 && j > 10 && k > 10)
>							continue;
>						else
>							yield return String.Format("{0} {1} {2}  Total {3}", i, j, k, ++Total);
>		}
>
>		static IEnumerable<string> ListPossibilities()
>		{
>			Total = 0;
>			int len = AlphaDigit.Length ;
>			Debug.Assert(AlphaDigit.Length == 62);
>			
>			char a, b, c ;
>			for( int i = 0; i < len; i++ )
>			{
>				a = AlphaDigit[i];
>				for( int j = 0; j < len; j++ )
>				{
>					b = AlphaDigit[j];
>					for (int k = 0; k < len; k++)
>					{
>						c = AlphaDigit[k];
>						if (!Char.IsDigit(a) && !Char.IsDigit(b) && !Char.IsDigit(c))
>							continue;
>						else
>							yield return String.Format("{0} {1} {2}  Total {3}", a, b, c, ++Total);
>					}
>				}
>			}
>
>		}
>		public static IEnumerable<string> GetValidPasswordList()
>		{
>			Total = 0;
>			for (int x = 1; x < 63; x++)
>			{
>				for (int y = 1; y < 63; y++)
>				{
>					for (int z = 0; z < ((y < 53 && x < 53) ? 63 : 11); z++) //24 seconds
>					//for (int z = 0; z < 63; z++ ) // 31 seconds
>					{
>						yield return string.Format("{0}.{1}.{2}  (Total:{3})", x, y, z, ++Total);
>					}
>				}
>			}
>		}
>
>		static double Password6()
>		{
>			decimal total = 0m;
>			int len = Alpha.Length;
>			for (int l1 = len; --l1 >= 0; )
>			{
>				char c1 = Alpha[l1];
>				Console.WriteLine(l1);
>				for (int l2 = len; --l2 >= 0; )
>				{
>					char c2 = Alpha[l2];
>
>					for (int l3 = len; --l3 >= 0; )
>					{
>						char c3 = Alpha[l3];
>
>						for (int l4 = len; --l4 >= 0; )
>						{
>							char c4 = Alpha[l4];
>
>							for (int l5 = len; --l5 >= 0; )
>							{
>								char c5 = Alpha[l5];
>
>								for (int l6 = len; --l6 >= 0; )
>								{
>									char c6 = Alpha[l6];
>
>									if (!Char.IsLower(c1)
>										&& !Char.IsLower(c2)
>										&& !Char.IsLower(c3)
>										&& !Char.IsLower(c4)
>										&& !Char.IsLower(c5)
>										&& !Char.IsLower(c6)
>									)
>										continue;
>
>									if (!Char.IsUpper(c1)
>										&& !Char.IsUpper(c2)
>										&& !Char.IsUpper(c3)
>										&& !Char.IsUpper(c4)
>										&& !Char.IsUpper(c5)
>										&& !Char.IsUpper(c6)
>									)
>										continue;
>
>									total++;
>								}
>
>							}
>						}
>					}
>
>				}
>
>			}
>			return (double)total;
>
>		}
>	}
>
>

Didn't have time to try this today. Hopefully tomorrow morning......