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How many ways are there to deal hands from a standard playing deck to four players if: 1. Each player gets exactly 13 cards. 2. Each player gets seven cards and the rest of the cards remain in the deck?

How many ways are there to deal hands from a standard playing deck to four players if: 1. Each player gets exactly 13 cards. 2. Each player gets seven cards and the rest of the cards remain in the deck?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This is a discrete math (counting techniques) problem. Please explain clearly, no cursive writing.

 

**Additional Instructions** For the exercises that ask you to answer "How many ...", express your results as a combinatorial formula, calculate the integer value that answers the question, and provide a short justification of your formula choice.
Transcribed Image Text:**Additional Instructions** For the exercises that ask you to answer "How many ...", express your results as a combinatorial formula, calculate the integer value that answers the question, and provide a short justification of your formula choice.
**Title: Dealing Cards from a Standard Playing Deck** **Introduction** In card games, distributing cards among players is a fundamental aspect that can be explored through combinatorial mathematics. A standard playing deck consists of 52 cards. Let's explore the problem of dealing hands to four players under different conditions. **Problem Statement** How many ways are there to deal hands from a standard playing deck to four players if: 1. Each player gets exactly 13 cards. 2. Each player gets seven cards and the rest of the cards remain in the deck. **Discussion** 1. **13 Cards per Player**: When dealing 13 cards to each player, the entire deck is distributed among the players, leaving no cards remaining. This scenario reflects a balanced distribution where each player has an equal share of the deck. 2. **Seven Cards per Player**: In this case, each player receives seven cards, totaling 28 cards, with the remaining 24 cards staying in the deck. This setup may be used in games that involve holding a smaller hand or in preliminary rounds. Understanding these distributions helps in strategizing and predicting possible outcomes in card games. Analyzing the mathematical possibilities also enriches one's grasp of probability and combinatorial theory.
Transcribed Image Text:**Title: Dealing Cards from a Standard Playing Deck** **Introduction** In card games, distributing cards among players is a fundamental aspect that can be explored through combinatorial mathematics. A standard playing deck consists of 52 cards. Let's explore the problem of dealing hands to four players under different conditions. **Problem Statement** How many ways are there to deal hands from a standard playing deck to four players if: 1. Each player gets exactly 13 cards. 2. Each player gets seven cards and the rest of the cards remain in the deck. **Discussion** 1. **13 Cards per Player**: When dealing 13 cards to each player, the entire deck is distributed among the players, leaving no cards remaining. This scenario reflects a balanced distribution where each player has an equal share of the deck. 2. **Seven Cards per Player**: In this case, each player receives seven cards, totaling 28 cards, with the remaining 24 cards staying in the deck. This setup may be used in games that involve holding a smaller hand or in preliminary rounds. Understanding these distributions helps in strategizing and predicting possible outcomes in card games. Analyzing the mathematical possibilities also enriches one's grasp of probability and combinatorial theory.
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