How to test if a non-repeated random name generator was implemented correctly?

My goal is to implement a test for a programming exercise. The exercise requires a method for generating random combinations of two uppercase letters and three digits (in that order, eg: QF354). The combinations must be random and non repeating.

How can I test if the method was implemented right?

I was thinking about generating a group of samples and to check for any repeated value, but the number of permutations is too large (p = 26*26*10*10*10 = 676000) for quick tests.

I don't know how big my group of samples should be to affirm (at least with high confidence) that the values are non-repeating. Alternatives are also welcome.