Probability

# Distinct Objects into Distinct Bins

There are 3 distinct pirates: Ned, Jack, and Blackbeard.
There are 4 distinct pieces of treasure: An emerald gemstone, a gold chalice, a silver necklace, and an ornamental saber.

How many ways are there to distribute the treasure among the pirates?

At an art auction, there are 7 distinct paintings on auction and 6 distinct bidders. One of those bidders, Leonard Block, will buy exactly 5 paintings.

How many distributions of the paintings are there if all paintings are sold?

There are 6 distinct prizes to be won in a raffle. The first winner gets to pick 3 of those prizes, the second winner gets to pick 2 of those prizes, and the third winner gets the prize that is left. There are 10 distinct people signed up for the raffle, and each person can win up to one time.

How many ways can the prizes be distributed?

Grandma Sue has 8 distinct candies that she will distribute among her 3 distinct grandchildren.

How many ways are there to distribute the candies if each grandchild receives at least two candies?

Sid and Betty found 9 distinct trading cards in their grandfather's attic. They flip a coin to decide who gets each card, but they also decide that each person should get at least one card.

How many distributions of the cards are possible?

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