Hello, amyl95!

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(1) How many different poker hands can be dealt to a player?

You are correct!

There are: . possible hands.

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(2) How many hands include the Ace of Spades?

We want the and four of the 51 other cards.

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(3) How many hands do not contain the Ace of Spades?

We want 5 of the other 51 cards.

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(4) How many hands include all 4 Aces?

There is one way to have all four Aces.

And we want one of the other 48 cards.

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(5) How many hands contain exactly 3 Aces?

There are choices for the three Aces.

And there are ways to choose the other two cards.

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