in how many ways can you make a four letter password?

Question

with the letters ABCD and E if you cannot repeat a character

Answer 1

You have 5 choices for the first letter.

Having chosen the first letter, you then have 4 choices for the 2nd letter. This means you have 5 x 4 = 20 choices for the first pair of letters.

Having chosen the first two letters, you then have 3 choices for the next letter; and so on.

The result is that there are 5 x 4 x 3 x 2 = 120 possibilities.

Answer 2

5!/(5-4)!
5!/1!
which is to say
5*4*3*2*1 all divided by 1,
so
120 ways