Here we have to assume that

Choose a card- it can, of course, be any thing. Replace it and choose another card. It can be anything except the first card- the probability of that is (k-1)/k. Replace it and choose a third card. It can be anything except the first 2- the probability of that is (k-2)/k. Doing this n times, we have .

What is the probability that you choose one of each card except one?

What is the probability that you choose one of each card except two?

More generally, find a probability function to calculate the probability of getting all except t cards of the set.