In how many ways could you choose two diffirent letters from the letters c, o,u, n,t

The first one you choose could be any one of the 5 letters.
             For each of them ...
The second one can be any one of the remaining 4 letters.

Total ways to pick out 2 letters = (5 x 4) = 20 .

BUT ...

There are two ways to pick each different pair of letters.
You could pick C-N or pick N-C, and you'd have the same pair
either way.

So, although there are 20 different ways to pick two  letters, there
are only (20/2) = 10 different pairs of letters you can end up with.