Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Permutations

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Permutations

Find the Computing Permutation.

$\displaystyle P (7, 5)$

Possible Answers:

5,100 $\displaystyle 5,100$

5,000 $\displaystyle 5,000$

5,400 $\displaystyle 5,400$

5,041 $\displaystyle 5,041$

2,520 $\displaystyle 2,520$

Correct answer:

2,520 $\displaystyle 2,520$

Explanation:

$\displaystyle P (7, 5)$

$\frac{7!}{(7 - 5)!} = \frac{7!}{2!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2!}{2!} = \frac{5,040}{2}=2520$ $\displaystyle \frac{7!}{(7 - 5)!} = \frac{7!}{2!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2!}{2!} = \frac{5,040}{2}=2520$

Report an Error

Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

An ice cream vendor sells five different flavors of ice cream.

In how many ways can you choose three scoops of different ice cream flavors if order matters?

Possible Answers:

$\displaystyle 60$

$5^{3}$ $\displaystyle 5^{3}$

$\displaystyle 35$

125 $\displaystyle 125$

$3^{5}$ $\displaystyle 3^{5}$

Correct answer:

$\displaystyle 60$

Explanation:

There are five ways to choose the first scoop, then four ways to choose the second scoop, and finally three ways to choose the third scoop:

5 * 4 * 3 = 60

Report an Error

Example Question #1 : How To Find The Missing Number In A Set

There are 5 men and 4 women competing for an executive body consisting of :

President
Vice President
Secretary
Treasurer

It is required that 2 women and 2 men must be selected

How many ways the executive body can be formed?

Possible Answers:

180 $\displaystyle 180$

1440 $\displaystyle 1440$

$\displaystyle 60$

120 $\displaystyle 120$

240 $\displaystyle 240$

Correct answer:

1440 $\displaystyle 1440$

Explanation:

2 men can be selected:

$C\binom{5}{2 } = 10$ $\displaystyle C\binom{5}{2 } = 10$

2 women can be selected out of 4 women:

$C\binom{4}{2} = 6$ $\displaystyle C\binom{4}{2} = 6$

Finally, after the selection process, these men and women can fill the executive body in 4!=24 $\displaystyle 4!=24$ ways.

This gives us a total of $10\times 6\times 24 = 1440$ $\displaystyle 10\times 6\times 24 = 1440$

Report an Error

Example Question #2 : Permutations

How many ways can a three committee board select the president, vice president and treasurer from a group of 15 people?

Possible Answers:

3375 $\displaystyle 3375$

2940 $\displaystyle 2940$

None of the above

2700 $\displaystyle 2700$

2730 $\displaystyle 2730$

Correct answer:

2730 $\displaystyle 2730$

Explanation:

In this problem, order is important because once someone is chosen as a position they can not be chosen again, and once a position is filled, no one else can fill that in mind.

The presidential spot has a possibility of 15 choices, then 14 choices for vice president and 13 for the treasurer.

So:

$\displaystyle 15*14*13=2730$

Report an Error

Example Question #2 : Permutations

How many ways can you re-arrange the letters of the word JUBILEE?

Possible Answers:

5,040 $\displaystyle 5,040$

5,460 $\displaystyle 5,460$

10,920 $\displaystyle 10,920$

2,520 $\displaystyle 2,520$

Correct answer:

2,520 $\displaystyle 2,520$

Explanation:

There are 7 letters in the word jubilee, so initially we can calculate that there are $\displaystyle 7! = 5,040$ ways to re-arrange those letters. However, The letter e appears twice, so we're double counting. Divide by 2 factorial (2) to get 2,520 $\displaystyle 2,520$ .

Report an Error

Example Question #3 : Permutations

How many ways can you re-arrange the letters of the word BANANA?

Possible Answers:

$\displaystyle 18$

$\displaystyle 20$

$\displaystyle 40$

$\displaystyle 60$

720 $\displaystyle 720$

Correct answer:

$\displaystyle 60$

Explanation:

At first, it makes sense that there are $\displaystyle 6! = 720$ ways to re-arrange these letters. However, the letter A appears 3 times and the letter N appears twice, so divide first by 3 factorial and then 2 factorial:

$\frac{720}{3! \cdot 2! } = \frac{720}{6 \cdot 2 } = \frac{720 } { 12} = 60$ $\displaystyle \frac{720}{3! \cdot 2! } = \frac{720}{6 \cdot 2 } = \frac{720 } { 12} = 60$

Report an Error

Example Question #42 : Algebra Ii

In a class of 24 students, how many distinct groups of 4 can be formed?

Possible Answers:

10,626 $\displaystyle 10,626$

1,153 $\displaystyle 1,153$

720 $\displaystyle 720$

$\displaystyle 6$

Correct answer:

10,626 $\displaystyle 10,626$

Explanation:

To solve, evaluate $\binom{24}{4} = \frac{24! }{4! \cdot 20!} = 10,626$

Report an Error

Example Question #42 : Algebra Ii

13 rubber ducks are competing in a race. How many different arrangements of first, second, and third place are possible?

Possible Answers:

1,716 $\displaystyle 1,716$

$\displaystyle 6$

$\displaystyle 1,037,836,800$

286 $\displaystyle 286$

$\displaystyle 3,628,800$

Correct answer:

1,716 $\displaystyle 1,716$

Explanation:

There are 3 winners out of the total set of 13. That means we're calculating $13P3 = \frac{13! }{(13-3)!} = \frac{13!}{10!} = 1,716$ $\displaystyle 13P3 = \frac{13! }{(13-3)!} = \frac{13!}{10!} = 1,716$

Report an Error

Example Question #3 : Permutations

7 students try out for the roles of Starsky and Hutch in a new school production. How many different ways can these roles be cast?

Possible Answers:

$\displaystyle 21$

120 $\displaystyle 120$

$\displaystyle 42$

$\displaystyle 5$

2,520 $\displaystyle 2,520$

Correct answer:

$\displaystyle 42$

Explanation:

There are 7 potential actors and 2 different roles to fill. This would be calculated as $\displaystyle 7!$ divided by $\displaystyle (7-2)! = 5!$ , or 42

Report an Error

Example Question #4 : Permutations

How many different 4 letter words can be made out of the letters A, B, C, D, and E?

Possible Answers:

$\displaystyle 20$

$\displaystyle 5$

$\displaystyle 60$

120 $\displaystyle 120$

480 $\displaystyle 480$

Correct answer:

120 $\displaystyle 120$

Explanation:

Since order matters, use the permutation formula:

$P(n,r)=\frac{n!}{(n-r)!}$ $\displaystyle P(n,r)=\frac{n!}{(n-r)!}$

There are 5 letters to choose from (n), and you pick 4 of them (r).

$P(5,4)=\frac{5!}{(5-4)!}=\frac{5*4*3*2*1}{1}=120$ $\displaystyle P(5,4)=\frac{5!}{(5-4)!}=\frac{5*4*3*2*1}{1}=120$

So there are 120 possible words that can be formed.

Report an Error

View Algebra 2 Tutors

John
Certified Tutor

Anderson University, Bachelor in Arts, Music Performance.

View Algebra 2 Tutors

Calvin
Certified Tutor

University of Southern California, Bachelor of Science, International Relations.

View Algebra 2 Tutors

Juana B.
Certified Tutor

The University of Texas Medical Branch, Bachelor of Science, Chemistry.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Philadelphia, GRE Tutors in Philadelphia, French Tutors in Denver, GMAT Tutors in Denver, Spanish Tutors in Dallas Fort Worth, LSAT Tutors in Philadelphia, GRE Tutors in Denver, English Tutors in San Diego, French Tutors in Philadelphia, Algebra Tutors in San Diego

Popular Courses & Classes

LSAT Courses & Classes in San Diego, GMAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in New York City, LSAT Courses & Classes in New York City, Spanish Courses & Classes in New York City, SAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Phoenix, ISEE Courses & Classes in Miami, SAT Courses & Classes in Philadelphia

Popular Test Prep

LSAT Test Prep in San Diego, SSAT Test Prep in Atlanta, ISEE Test Prep in Philadelphia, GMAT Test Prep in New York City, ISEE Test Prep in Denver, LSAT Test Prep in Miami, ISEE Test Prep in Seattle, LSAT Test Prep in New York City, GRE Test Prep in Philadelphia, SSAT Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Permutations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Permutations

Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

Example Question #1 : How To Find The Missing Number In A Set

Example Question #2 : Permutations

Example Question #2 : Permutations

Example Question #3 : Permutations

Example Question #42 : Algebra Ii

Example Question #42 : Algebra Ii

Example Question #3 : Permutations

Example Question #4 : Permutations

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: