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If a coin is flipped twenty times, how many ways are there to get exactly ten tails and ten heads?

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.

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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.

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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.

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