We have k envelopes numbered 1 to k and n typed letters that are numbered 1 to n.

In each envelope, we may put from 0 up to n letters.

(i) Under the above assumptions, in how many different ways the letters may be put into the envelopes?

(ii) For 1 ≤ k ≤ n, and assuming that the allocation of the letters to the envelopes is completely random, what is the probability that an envelope will contain two or more letters?