Postcards and Postboxes

Tommy Wallach wrote:Hey Gughan,

This is a weird sort of combinatorics question, which I would solve with the slots method:

1. Find # of slots (decisions to be made)
2. Fill in possibilities at each decision point
3. Figure out if Order matters or not (or a hybrid)
4. If order matters, multiply all slots together; if order doesn't matter, multiply all slots and divide by # of slots factorial wherever order doesn't matter.

In this case, we have to make 10 decisions, because every postcard has to be mailed. We need to decide which of the 6 mailboxes to put each mailbox in.

_ _ _ _ _ _ _ _ _ _

For each postcard, we have 6 choices. This pool never drops down (as it does in most combinatorics questions), because there's no limit to how many postcards we can put in each letterbox:

6 6 6 6 6 6 6 6 6 6

The answer is thus [spoiler]6^10[/spoiler].

-t