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A player is dealt 4 cards from a standard 52 -card deck. Determine the probability of being dealt three of a kind (such as three aces or three kings) by answering questions a through d.
a) How many ways can 4 cards be selected from a 52 -card deck?
There are ways that 4 cards can be selected from a 52 -card deck.
(Type a whole number.)

Ask by Delgado Herrera. in the United States
Mar 25,2025

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There are 270,725 ways to select 4 cards from a 52-card deck.

Solución

The number of ways to choose 4 cards from a 52‑card deck is determined by the combination formula:
There are ways that 4 cards can be selected from a 52‑card deck.

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The Deep Dive

The total number of ways to select 4 cards from a 52-card deck can be calculated using the combination formula . Plugging in and , we find the number of combinations to be 270725.
So, there are 270725 ways that 4 cards can be selected from a 52-card deck.
Did you know that the game of poker can be traced back to the 10th century in China? It was a complex card game that evolved into many versions over the centuries, leading us to the popular versions we know today, like Texas Hold’em!
Practical applications of understanding probabilities extend beyond gaming. For example, in finance, professionals use probabilities when assessing risk and return on investments. Understanding these concepts can vastly improve decision-making and predicting outcomes!

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