**Question.**

We have k distinct postcards and want to send them all to our friends ( a friend can get any number of postcards, including 0). How many ways can this be done? What happens if we want to send at least one card to each friend?

**Hint:**

Decide now about the postcards. The answer to this question is .

**Solution:**

**I. **We have to decide about the postcards independently. Any postcard can be sent to any of the n friends. Hence, the result if .

**II. **Let be the cards. The set must be split into n disjoint non-empty sets . Thus, is a partition of S. From any partition of S into n (non-empty) classes we get possibilities to send out the postcards. Hence, the answer is .

More later,

Nalin Pithwa

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