menu
bartleby
search
close search
Hit Return to see all results
Subscribe
Sign in

Math
Discrete Mathematics With Applications5th Edition

close solutoin list
Chapter 9.5, Problem 30ES
BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Solutions

Chapter
Section
Problem 1TY
Problem 2TY
Problem 3TY
Problem 4TY
Problem 5TY
Problem 1ES
Problem 2ES
Problem 3ES
Problem 4ES
Problem 5ES
Problem 6ES
Problem 7ES
Problem 8ES
Problem 9ES
Problem 10ES
Problem 11ES
Problem 12ES
Problem 13ES
Problem 14ES
Problem 15ES
Problem 16ES
Problem 17ES
Problem 18ES
Problem 19ES
Problem 20ES
Problem 21ES
Problem 22ES
Problem 23ES
Problem 24ES
Problem 25ES
Problem 26ES
Problem 27ES
Problem 28ES
Problem 29ES
Problem 30ES
BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
4 views

Find the error in the following reasoning: “Consider forming a poker hand with two pairs as a five-step process.”
Step 1: Choose the denomination of one of the pairs.
Step 2: Choose the two cards of that denomination.
Step 3: Choose the denomination of the other of the pairs.
Step 4: Choose the two cards of that second denomination.
Step 5: Choose the fifth card from the remaining denominations.
There are ( 13 1 ) ways to perform step 1, ( 4 2 ) ways to perform step 2, ( 12 1 ) ways to perform step 3, ( 4 2 ) ways to perform step 4, and ( 44 1 ) ways to perform step 5. Therefore, the total number of five-card poker hands with two pairs is 13 ⋅ 6 ⋅ 12 ⋅ 6 ⋅ 44 = 247.104. "

To determine

To find out the error in the given reasoning.

Explanation

Given information:

“Consider forming a poker hand with two pairs as a five-step process.

Step 1- Choose the denomination of one of the pairs.

Step 2- Choose the two cards of that denomination.

Step 3- choose the denomination of the other of pairs.

Step 4- choose the two cards of that second denomination.

Step 5- choose the fifth card from the remaining denominations.

There are (131) ways to perform step 1, (42) ways to perform the step 2, (121) ways to perform step 3, (42) ways to perform step 4, and (441) ways to perform step 5. Therefore the total number of five-card poker hands with two pairs is 13⋅6⋅12⋅6⋅44=247,104 .”

Calculation:

To form a poker hand with two pairs as a five-step process can be done as follows-

There are total 13 denominations in a deck of 52 cards. There are total 4 cards in each denomination.

The question is about forming a poker hand with two pairs. So in the Step 1 only, the two pairs of the denomination should be chosen.

Step 1- Choosing the denomination of one of the pairs. Since there are 13 denominations, so choosing 1 can be done in (131) ways but there is a need to choose the two pairs not one pair so this step is incorrect. It should have been choosing two pairs from 13 denominations in (132) ways.

Step2- Since there are total 4 cards in each denomination. So choosing the two cards from the same denomination can be done in (42) ways.So the step 2 is correct

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 9.5,
Problem 29ES
Chapter 9.6,
Problem 1TY
arrow_forward

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 9 Solutions

Show all chapter solutions add
Sect-9.1 P-1TYSect-9.1 P-2TYSect-9.1 P-3TYSect-9.1 P-4TYSect-9.1 P-1ESSect-9.1 P-2ESSect-9.1 P-3ESSect-9.1 P-4ESSect-9.1 P-5ESSect-9.1 P-6ES
Sect-9.1 P-7ESSect-9.1 P-8ESSect-9.1 P-9ESSect-9.1 P-10ESSect-9.1 P-11ESSect-9.1 P-12ESSect-9.1 P-13ESSect-9.1 P-14ESSect-9.1 P-15ESSect-9.1 P-16ESSect-9.1 P-17ESSect-9.1 P-18ESSect-9.1 P-19ESSect-9.1 P-20ESSect-9.1 P-21ESSect-9.1 P-22ESSect-9.1 P-23ESSect-9.1 P-24ESSect-9.1 P-25ESSect-9.1 P-26ESSect-9.1 P-27ESSect-9.1 P-28ESSect-9.1 P-29ESSect-9.1 P-30ESSect-9.1 P-31ESSect-9.1 P-32ESSect-9.1 P-33ESSect-9.2 P-1TYSect-9.2 P-2TYSect-9.2 P-3TYSect-9.2 P-4TYSect-9.2 P-5TYSect-9.2 P-6TYSect-9.2 P-1ESSect-9.2 P-2ESSect-9.2 P-3ESSect-9.2 P-4ESSect-9.2 P-5ESSect-9.2 P-6ESSect-9.2 P-7ESSect-9.2 P-8ESSect-9.2 P-9ESSect-9.2 P-10ESSect-9.2 P-11ESSect-9.2 P-12ESSect-9.2 P-13ESSect-9.2 P-14ESSect-9.2 P-15ESSect-9.2 P-16ESSect-9.2 P-17ESSect-9.2 P-18ESSect-9.2 P-19ESSect-9.2 P-20ESSect-9.2 P-21ESSect-9.2 P-22ESSect-9.2 P-23ESSect-9.2 P-24ESSect-9.2 P-25ESSect-9.2 P-26ESSect-9.2 P-27ESSect-9.2 P-28ESSect-9.2 P-29ESSect-9.2 P-30ESSect-9.2 P-31ESSect-9.2 P-32ESSect-9.2 P-33ESSect-9.2 P-34ESSect-9.2 P-35ESSect-9.2 P-36ESSect-9.2 P-37ESSect-9.2 P-38ESSect-9.2 P-39ESSect-9.2 P-40ESSect-9.2 P-41ESSect-9.2 P-42ESSect-9.2 P-43ESSect-9.2 P-44ESSect-9.2 P-45ESSect-9.2 P-46ESSect-9.2 P-47ESSect-9.3 P-1TYSect-9.3 P-2TYSect-9.3 P-3TYSect-9.3 P-4TYSect-9.3 P-5TYSect-9.3 P-1ESSect-9.3 P-2ESSect-9.3 P-3ESSect-9.3 P-4ESSect-9.3 P-5ESSect-9.3 P-6ESSect-9.3 P-7ESSect-9.3 P-8ESSect-9.3 P-9ESSect-9.3 P-10ESSect-9.3 P-11ESSect-9.3 P-12ESSect-9.3 P-13ESSect-9.3 P-14ESSect-9.3 P-15ESSect-9.3 P-16ESSect-9.3 P-17ESSect-9.3 P-18ESSect-9.3 P-19ESSect-9.3 P-20ESSect-9.3 P-21ESSect-9.3 P-22ESSect-9.3 P-23ESSect-9.3 P-24ESSect-9.3 P-25ESSect-9.3 P-26ESSect-9.3 P-27ESSect-9.3 P-28ESSect-9.3 P-29ESSect-9.3 P-30ESSect-9.3 P-31ESSect-9.3 P-32ESSect-9.3 P-33ESSect-9.3 P-34ESSect-9.3 P-35ESSect-9.3 P-36ESSect-9.3 P-37ESSect-9.3 P-38ESSect-9.3 P-39ESSect-9.3 P-40ESSect-9.3 P-41ESSect-9.3 P-42ESSect-9.3 P-43ESSect-9.3 P-44ESSect-9.3 P-45ESSect-9.3 P-46ESSect-9.3 P-47ESSect-9.3 P-48ESSect-9.3 P-49ESSect-9.4 P-1TYSect-9.4 P-2TYSect-9.4 P-3TYSect-9.4 P-3ESSect-9.4 P-4ESSect-9.4 P-5ESSect-9.4 P-6ESSect-9.4 P-7ESSect-9.4 P-8ESSect-9.4 P-9ESSect-9.4 P-10ESSect-9.4 P-11ESSect-9.4 P-12ESSect-9.4 P-13ESSect-9.4 P-14ESSect-9.4 P-15ESSect-9.4 P-16ESSect-9.4 P-17ESSect-9.4 P-18ESSect-9.4 P-19ESSect-9.4 P-20ESSect-9.4 P-21ESSect-9.4 P-22ESSect-9.4 P-23ESSect-9.4 P-24ESSect-9.4 P-25ESSect-9.4 P-26ESSect-9.4 P-27ESSect-9.4 P-28ESSect-9.4 P-29ESSect-9.4 P-30ESSect-9.4 P-31ESSect-9.4 P-32ESSect-9.4 P-33ESSect-9.4 P-34ESSect-9.4 P-35ESSect-9.4 P-36ESSect-9.4 P-37ESSect-9.4 P-38ESSect-9.4 P-39ESSect-9.4 P-40ESSect-9.5 P-1TYSect-9.5 P-2TYSect-9.5 P-3TYSect-9.5 P-4TYSect-9.5 P-5TYSect-9.5 P-1ESSect-9.5 P-2ESSect-9.5 P-3ESSect-9.5 P-4ESSect-9.5 P-5ESSect-9.5 P-6ESSect-9.5 P-7ESSect-9.5 P-8ESSect-9.5 P-9ESSect-9.5 P-10ESSect-9.5 P-11ESSect-9.5 P-12ESSect-9.5 P-13ESSect-9.5 P-14ESSect-9.5 P-15ESSect-9.5 P-16ESSect-9.5 P-17ESSect-9.5 P-18ESSect-9.5 P-19ESSect-9.5 P-20ESSect-9.5 P-21ESSect-9.5 P-22ESSect-9.5 P-23ESSect-9.5 P-24ESSect-9.5 P-25ESSect-9.5 P-26ESSect-9.5 P-27ESSect-9.5 P-28ESSect-9.5 P-29ESSect-9.5 P-30ESSect-9.6 P-1TYSect-9.6 P-2TYSect-9.6 P-3TYSect-9.6 P-1ESSect-9.6 P-2ESSect-9.6 P-3ESSect-9.6 P-4ESSect-9.6 P-5ESSect-9.6 P-6ESSect-9.6 P-7ESSect-9.6 P-8ESSect-9.6 P-9ESSect-9.6 P-10ESSect-9.6 P-11ESSect-9.6 P-12ESSect-9.6 P-13ESSect-9.6 P-14ESSect-9.6 P-15ESSect-9.6 P-16ESSect-9.6 P-17ESSect-9.6 P-18ESSect-9.6 P-19ESSect-9.6 P-20ESSect-9.6 P-21ESSect-9.7 P-1TYSect-9.7 P-2TYSect-9.7 P-3TYSect-9.7 P-4TYSect-9.7 P-5TYSect-9.7 P-6TYSect-9.7 P-7TYSect-9.7 P-1ESSect-9.7 P-2ESSect-9.7 P-3ESSect-9.7 P-4ESSect-9.7 P-5ESSect-9.7 P-6ESSect-9.7 P-7ESSect-9.7 P-8ESSect-9.7 P-9ESSect-9.7 P-10ESSect-9.7 P-11ESSect-9.7 P-12ESSect-9.7 P-13ESSect-9.7 P-14ESSect-9.7 P-15ESSect-9.7 P-16ESSect-9.7 P-17ESSect-9.7 P-18ESSect-9.7 P-19ESSect-9.7 P-20ESSect-9.7 P-21ESSect-9.7 P-22ESSect-9.7 P-23ESSect-9.7 P-24ESSect-9.7 P-25ESSect-9.7 P-26ESSect-9.7 P-27ESSect-9.7 P-28ESSect-9.7 P-29ESSect-9.7 P-30ESSect-9.7 P-31ESSect-9.7 P-32ESSect-9.7 P-33ESSect-9.7 P-34ESSect-9.7 P-35ESSect-9.7 P-36ESSect-9.7 P-37ESSect-9.7 P-38ESSect-9.7 P-39ESSect-9.7 P-40ESSect-9.7 P-41ESSect-9.7 P-42ESSect-9.7 P-43ESSect-9.7 P-44ESSect-9.7 P-45ESSect-9.7 P-46ESSect-9.7 P-47ESSect-9.7 P-48ESSect-9.7 P-49ESSect-9.7 P-50ESSect-9.7 P-51ESSect-9.7 P-52ESSect-9.7 P-53ESSect-9.7 P-54ESSect-9.7 P-55ESSect-9.8 P-1TYSect-9.8 P-2TYSect-9.8 P-3TYSect-9.8 P-4TYSect-9.8 P-5TYSect-9.8 P-1ESSect-9.8 P-2ESSect-9.8 P-3ESSect-9.8 P-4ESSect-9.8 P-5ESSect-9.8 P-6ESSect-9.8 P-7ESSect-9.8 P-8ESSect-9.8 P-9ESSect-9.8 P-10ESSect-9.8 P-11ESSect-9.8 P-12ESSect-9.8 P-13ESSect-9.8 P-14ESSect-9.8 P-15ESSect-9.8 P-16ESSect-9.8 P-17ESSect-9.8 P-18ESSect-9.8 P-19ESSect-9.8 P-20ESSect-9.8 P-21ESSect-9.8 P-22ESSect-9.8 P-23ESSect-9.9 P-1TYSect-9.9 P-2TYSect-9.9 P-3TYSect-9.9 P-4TYSect-9.9 P-1ESSect-9.9 P-2ESSect-9.9 P-3ESSect-9.9 P-4ESSect-9.9 P-5ESSect-9.9 P-6ESSect-9.9 P-7ESSect-9.9 P-8ESSect-9.9 P-9ESSect-9.9 P-10ESSect-9.9 P-11ESSect-9.9 P-12ESSect-9.9 P-13ESSect-9.9 P-14ESSect-9.9 P-15ESSect-9.9 P-16ESSect-9.9 P-17ESSect-9.9 P-18ESSect-9.9 P-19ESSect-9.9 P-20ESSect-9.9 P-21ESSect-9.9 P-22ESSect-9.9 P-23ESSect-9.9 P-24ESSect-9.9 P-25ESSect-9.9 P-26ESSect-9.9 P-27ESSect-9.9 P-28ESSect-9.9 P-29ESSect-9.9 P-30ESSect-9.9 P-31ESSect-9.9 P-32ESSect-9.9 P-33ESSect-9.9 P-34ES
bartleby
© bartleby 2019