Call Now to Set Up Tutoring:

(888) 888-0446

GRE Subject Test: Math : Combinational Analysis

Study concepts, example questions & explanations for GRE Subject Test: Math

Create An Account

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 Next →

Example Question #1 : Factorials

Simplify the following expression:

$\frac{12!}{10!-4!}$

Possible Answers:

121

123.004

132.0009

132

366

Correct answer:

132.0009

Explanation:

Recall that ! means facotrial in math. This means we multiply the number by all positive integers less than itself. In other words, this...

$\frac{12!}{10!-4!}$

Becomes

$\frac{1\cdot 2\cdot3\cdot 4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10)-(1\cdot2\cdot3\cdot 4)}$

This is a great job for a calculator, which yields:

132.0009

Report an Error

Example Question #1 : Factorials

Evaluate: 5!-3(4!)

Possible Answers:

Correct answer:

Explanation:

Step 1: We need to define factorial (!). The operation (!) means that you multiply the number next to the ! by the next consecutive number down to 1.

Step 2: Expand the equation:

$5!=5\cdot4\cdot3\cdot2\cdot1=120$
3(4!)= $3(4\cdot 3\cdot 2\cdot 1)=3(24)=72$

Step 3: Evaluate the expression:

120-72=48

The answer to the expression is .

Report an Error

Example Question #1 : Factorials

$\frac{5!}{3!-2!}$

Possible Answers:

Correct answer:

Explanation:

is the product of consecutive numbers 1 through

$\frac{5\times 4\times 3\times 2\times 1}{(3\times 2\times 1)-(2\times 1)} =$

$\frac{120}{6-2} = \frac{120}{4} = 30$

Report an Error

Example Question #2 : Factorials

6! - 2(3!)

Possible Answers:

708

700

720

Correct answer:

708

Explanation:

is the product of consecutive numbers 1 through

$(6\times 5\times 4\times 3\times 2\times 1) - 2(3\times 2\times 1) =$

720 - 2(6) = 720 -12 = 708

Report an Error

Example Question #1 : Factorials

Evaluate: $\frac {13!}{10!}$

Possible Answers:

1716

1796

1776

1736

Correct answer:

1716

Explanation:

Step 1: Rewrite the equation by using rule of factorials...

Rule of factorials: Multiply the number in front of factorial and each number one lower than the rest until I hit .

$\frac {13!}{10!}=\frac {13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

Step 2: Reduce any common numbers (colored in blue):

$\frac {13\cdot 12\cdot 11\cdot {\color{Blue} 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}{{\color{Blue} 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}$

We get $13\cdot12\cdot11$ !

Step 3: Evaluate what's left

$13\cdot12\cdot11=1716$

The value of the fraction is 1716 .

Report an Error

Example Question #1 : Factorials

What is $_{8}P_{4}$ equal to?

Possible Answers:

1,640

1,580

1,680

1,600

Correct answer:

1,680

Explanation:

_nP_k depicts the permutation of n total objects with k objects being arranged.

Thus,

$_{8}P_{4} = \frac{n!}{k!}=\frac{8!}{4!}$

The upper factorial is the upper index, and the lower factorial is the difference of the indices.

$\frac{8!}{4!} = \frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{4\times 3\times 2\times 1}$

The or $4\times3\times2\times1$ will cancel out.

$8\times7\times6\times5 = 56\times30 = 1,680$

Report an Error

Example Question #1 : Combinational Analysis

Twelve horses run a race. In how many ways can 3 horses finish in 1st, 2nd, and 3rd place, in any order?

Possible Answers:

225

220

230

200

Correct answer:

220

Explanation:

This particular question is asking one to find the combination. This is because the order of the 1st, 2nd, and 3rd place finishers is not important.

Thus evaluate $_{12}C_{3}$ .

$_{12}C_{3} = \frac{12!}{(12-3)! 3!}$

Because 12! and both consist of , the will cancel out leaving:

$\frac{12\times 11\times 10}{3\times 2\times 1}$

$\frac{12\times 11\times 10}{3\times 2\times 1} = \frac{1320}{6} = 220$

Report an Error

Example Question #1 : Factorials

Evaluate: 10!-4(9!)+8!-3(7!)

Possible Answers:

2202480

2900000

3000000

2928250

Correct answer:

2202480

Explanation:

Step 1: Evaluate 10!

$10!=10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=3628800$

Step 2: Evaluate 4(9!)

$4(9!)=4(9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)=1451520$

Step 3: Evaluate

$8!=8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=40320$

Step 4: Evaluate 3(7!)

$3(7!)=3(7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)=15120$

Step 5: Add/Subtract values:

3628800-1451520+40320-15120=2202480

Report an Error

Example Question #1 : Factorials

Evaluate: $3\cdot \bigg[\frac {9!}{7!}\bigg]$

Possible Answers:

243

225

289

216

Correct answer:

216

Explanation:

Step 1: Do the division of the factorials

$\bigg[\frac {9!}{7!}\bigg]=\frac {9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

Step 2: Simplify by cancelling out any terms on both top and bottom:

$\frac {9\cdot 8\cdot {\color{Blue} 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}{{\color{Blue} 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}=9\cdot8=72$

Step 3: Multiply the result of the division by 3..

$72 \cdot 3=216$

The value of that expression is 216 .

Report an Error

Example Question #1 : Factorials

Evaluate: 7!-6(6!)

Possible Answers:

Correct answer:

Explanation:

Step 1: Find

$7!=7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=5040$

Step 2: Find 6(6!)

$6(6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)=6(720)=4320$

Step 3: Subtract the values from step 1 and step 2:

5040-4320=720=6!

The answer is

Report an Error

← Previous 1 2 3 4 5 6 Next →

View Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View Tutors

Midori
Certified Tutor

University of Connecticut, Bachelor in Arts, Applied Mathematics. University of Southern California, Master of Arts Teaching,...

All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Philadelphia, Biology Tutors in Denver, English Tutors in Miami, Chemistry Tutors in New York City, Computer Science Tutors in Miami, ACT Tutors in New York City, ACT Tutors in Philadelphia, Reading Tutors in San Diego, Physics Tutors in Atlanta, GMAT Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, SAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, ACT Courses & Classes in Houston, SAT Courses & Classes in Houston, SAT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Seattle, LSAT Courses & Classes in Chicago, ACT Courses & Classes in Seattle

Popular Test Prep

ACT Test Prep in Philadelphia, ISEE Test Prep in Atlanta, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Chicago, SSAT Test Prep in Boston, SAT Test Prep in Houston, ACT Test Prep in Seattle, LSAT Test Prep in Miami, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in New York City

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

GRE Subject Test: Math : Combinational Analysis

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #2 : Factorials

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #1 : Combinational Analysis

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #1 : Factorials

All GRE Subject Test: Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: