+118677 4 letters are chosen from the alphabet. And these are supposed to be the number of possibilities but something is wrong!
Letters all different = 26*25*24*23=358800
letters 2 the same= 26*1*25*24*6= 93600
letters 3 the same=26*1*1*25*4=2600
Letters all the same=26
Add all these and I get 455026
Now I know it should add up to 264=456976 so I am short a few possibilities here.
WHY AM I SHORT???
NOTE: 456976-455026=1950=25*26*3 (does this help?)
This sort of imples that the 3 letters all the same is *12 not *4 but that does not make sense to me. 
+893 Hi Melody
Your second category, two letters the same, covers the possibility that two letters are the same and that the other two letters are different and different from each other. In other words, it doesn't allow for the possibility that your four letters consist of just two letters forming two pairs. This produces another 1950 combinations. You have to be quite careful as to how you calculate this, it is potentially confusing and it's very easy to overcount.
+893 Hi Melody
Your missing combinations are in your 'two the same' section. You also have to include contributions from two the same and the other two the same as well, (and you have to be careful as to the calculation of that number).
+893 Hi Melody
Your second category, two letters the same, covers the possibility that two letters are the same and that the other two letters are different and different from each other. In other words, it doesn't allow for the possibility that your four letters consist of just two letters forming two pairs. This produces another 1950 combinations. You have to be quite careful as to how you calculate this, it is potentially confusing and it's very easy to overcount.
+118677 Okay, I get you. Thanks Bertie.
This tell me my missing category that is certainly true but the permutations are still causing problems.
I think that I have it all sorted now.
4 letters are chosen from the alphabet. And these are supposed to be the number of possibilities but something is wrong!
Letters all different = 26*25*24*23=358800
letters 2 the same and other 2 different= 26*1*25*24*4C2= 93600
letters 2 pairs = 26*1*25*1*4C2 divided by a half (got it) = 1950
I had to halve it because for each pair left there are 2 that are the same.
letters 3 the same=26*1*1*25*4C3=2600
Letters all the same=26
Now I know it should add up to 264=456976 and they do so that is great!
