Discrete Mathematics
# Combinations

A bakery sells three kinds of pastries: donuts, muffins, and cookies. If you go to the store to buy $28$ pastries, how many different combinations of them can you buy if they only have $27$ of each type available?

**Details and assumptions**

All the pastries of one type are indistinguishable.

Cards for a trading card game can be purchased in packages of 6 cards, of which exactly 1 of them is a rare card.

If there are a total of 8 rare cards that can be collected, and you purchase $3$ packages of cards, how many different combinations of the rare cards could you end up with?

For example, you could have 1 of the second rare cards, and the rest are the eighth rare card.

You have 6 identical balls and 6 (distinct) boxes numbered $1$ through $6.$ How many ways can the 6 balls be distributed amongst the boxes?

**Details and assumptions**

Some of the boxes can be empty.