Question
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 270,725 ways that 4 cards can be selected from a 52 -card deck.
(Type a whole number.)
b) Each deck contains 4 twos, 4 threes, and so on. How many ways can three of the same card be selected from the deck?
There are 52 ways that three of the same card can be selected from the deck.
(Type a whole number.)
c) The remaining card must be different from the 3 chosen. After selecting the three of a kind, there are 12 different ranks of cards remaining in the deck that can be chosen. Of the 12 ranks remaining, the
player chooses 1 of them and then selects one of the 4 cards in the chosen rank. How many ways can the player select the remaining card?
There are
(Type a whole number.)
a) How many ways can 4 cards be selected from a 52 -card deck?
There are 270,725 ways that 4 cards can be selected from a 52 -card deck.
(Type a whole number.)
b) Each deck contains 4 twos, 4 threes, and so on. How many ways can three of the same card be selected from the deck?
There are 52 ways that three of the same card can be selected from the deck.
(Type a whole number.)
c) The remaining card must be different from the 3 chosen. After selecting the three of a kind, there are 12 different ranks of cards remaining in the deck that can be chosen. Of the 12 ranks remaining, the
player chooses 1 of them and then selects one of the 4 cards in the chosen rank. How many ways can the player select the remaining card?
There are
(Type a whole number.)
Ask by Sanders Morgan. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 270,725 ways to select 4 cards from a 52-card deck. There are 52 ways to select three of the same card. After choosing three of a kind, there are 48 ways to select the remaining card.
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Beyond the Answer
To determine how many ways the player can select the remaining card, first, we note that there are 12 different ranks left after selecting three of a kind. For each of these ranks, there are 4 cards available. Thus, the total number of ways to select that remaining card is calculated by multiplying the number of ranks by the 4 available cards in each rank. Therefore, there are 48 ways the player can select the remaining card.
Additionally, it’s fascinating to consider that the concept of probability and card games dates back centuries! The earliest known reference to a deck of cards can be traced back to China in the 9th century. Over time, different cultures adapted and modified the design, eventually leading to the standard 52-card deck we are familiar with today. Isn’t it intriguing how games such as poker and bridge have evolved and sparked competitive spirit across the globe?
