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How many different 5-card poker hands can be dealt from a regular 52-card deck?

User Jms Bnd
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1 Answer

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Final answer:

There are 2,598,960 different 5-card poker hands that can be dealt from a 52-card deck, calculated using the combination formula C(52, 5).

Step-by-step explanation:

The student asks about the number of different 5-card poker hands that can be dealt from a regular 52-card deck. The calculation for this involves combinatorics, specifically the combination formula which is represented as 'n choose k' or C(n, k), where n is the total number of items, and k is the number of items to choose.

The total number of ways to pick 5 cards out of 52 without regard to order (since the order in a poker hand doesn't matter) is calculated as follows:


C(52, 5) = 52! / [5! * (52 - 5)!]

This simplifies to:


2,598,960 different 5-card poker hands

Therefore, the answer to the student's question is that there are 2,598,960 different 5-card poker hands that can be dealt from a standard 52-card deck.

User Digiarnie
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