Concept explainers
a.
To calculate: The number of 5 card hands are possible that have 3 hearts and 2 clubs from a deck of 52 cards.
a.
Answer to Problem 45E
The number of 5 card hands are possible that have 3 hearts and 2 clubs from a deck of 52 cardsare
Explanation of Solution
Given information:
There is deck of 52 cards. 5 cards combinations must be there with 3 hearts and 2 clubs.
Formula used:
If there are n objects taken r at a time then combination is defined as
Calculation:
Consider the provided information that there is deck of 52 cards. 5 cards combinations must be there with 3 hearts and 2 clubs.
In a deck of 52 cards there 13 hearts and 13 clubs.
3 cards of heart and 2 of clubs are to be selected, use combination as selection does not matter.
The possible ways are
Recall that if there are n objects taken r at a time then combination is defined as
Here n is 13and r is 3 for
Thus, the number of 5 card hands are possible that have 3 hearts and 2 clubs from a deck of 52 cards are
b.
To calculate: The number of 5 card hands are possible that have 1 ace, 2 jacks and 2 kings from a deck of 52 cards.
b.
Answer to Problem 45E
The number of 5 card hands are possible that have 1 ace, 2 jacks and 2 kings from a deck of 52 cards are
Explanation of Solution
Given information:
There is deck of 52 cards. 5 cards combinations must be there with 1 ace, 2 jacks and 2 kings.
Formula used:
If there are n objects taken r at a time then combination is defined as
Calculation:
Consider the provided information that there is deck of 52 cards. 5 cards combinations must be there with 1 ace, 2 jacks and 2 kings.
In a deck of 52 cards there 4 aces, 4 jacks and 4 kings.
1 ace, 2 jacks and 2 kings are to be selected, use combination as selection does not matter.
The possible ways are
Recall that if there are n objects taken r at a time then combination is defined as
Here n is 4 and r is 1 for
Thus, the number of 5 card hands are possible that have 1 ace, 2 jacks and 2 kings from a deck of 52 cards are
c.
To calculate: The number of 5 card hands are possible that have all face cards from a deck of 52 cards.
c.
Answer to Problem 45E
The number of 5 card hands are possible that have all face cardsfrom a deck of 52 cards are
Explanation of Solution
Given information:
There is deck of 52 cards. 5 cards combinations must be there with all face cards.
Formula used:
If there are n objects taken r at a time then combination is defined as
Calculation:
Consider the provided information that there is deck of 52 cards. 5 cards combinations must be there with all face cards.
In a deck of 52 cards there 12 face cards.
All face cardsare to be selected, use combination as selection does not matter.
The possible ways are
Recall that if there are n objects taken r at a time then combination is defined as
Here n is 12 and r is 5for
Thus, the number of 5 card hands are possible that have all face cardsfrom a deck of 52 cards are
Chapter 13 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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