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Numerade Educator

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Problem 12 Medium Difficulty

Tell whether each situation is a permutation or combination.
How many 5 -card hands can be dealt from a standard deck of 52 cards?

Answer

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Alayna H.

McMaster University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

So we have 52 cards and we need five of them. It doesn't matter whether we get two sevens and then 383 eights and then two sevens. It's the same hand. So this is gonna be a combination where we have 52 cards and we're choosing five of them. So this is gonna be 52 times 51 times 50 times 49 times 48 now because we could have the same five cards in our hands. But given to us in a different order and it's still the same hand you got, remember to take off those duplications, and so that gives me on the top of this a nice long member on the bottom of got 120. And so when I divide this, the number of possible hands that I can have is gonna be two million 598,000 960 possible five card hands from the deck of 52

University of Louisville
Top Algebra Educators
GH
Grace H.

Numerade Educator

Alayna H.

McMaster University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor