How many 3 letters-long codes can be made by 5 different letters? You have five letters: C, H, E, S, T
How many different codes, consisting of three letters, can be made from the above letters?
I'd say ${5}\choose{3}$ is the correct answer, since the order of the letters doesn't matter. Is this (that the order doesn't matter) why $\frac{5!}{3!}$ isn't the correct answer?

Letters can be repeated. The first letter can be chosen from 5 different letters, so can the second and third letter. Thus the answer is $5^{3} = 125$ different codes.
Thank you @Yinon Eliraz!
