In a game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand. What is the probability that a player is dealt 2 hearts? What is the probability that a player is dealt 4 kings?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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In a game of euchre, the deck consists of the 9, 10, jack, queen, king and ace of each suit. Players are dealt a five card hand. What is the probability that a player is dealt 2 hearts? What is the probability that a player is dealt 4 kings?

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Step 1

(a)

Obtain the probability that the player is dealt with 2 hearts.

The probability that the player is dealt with 2 hearts is obtained below as follows:

 

From the information, given that the deck consists of the 9, 10, jack, queen, king and ace of each suit. That is, there are 4 suits in each deck(spade, clubs, heart, diamond).

 

That is, there are two red suits (hearts and diamonds) and the two black suits(spade, clubs).

The total number of hearts =6.

Also given that players are dealt a five card hand.

 

Let S denotes the total number of cards.

That is,

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