• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the value of 22C19? tagged by: Max@Math Revolution ##### This topic has 4 expert replies and 1 member reply ### GMAT/MBA Expert ## What is the value of 22C19? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] What is the value of 22C19? A. 770 B. 1540 C. 3080 D. 4620 E. 6160 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Email to : info@mathrevolution.com

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12663 messages
Followed by:
1246 members
5254
GMAT Score:
770
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the value of 22C19?

A. 770
B. 1540
C. 3080
D. 4620
E. 6160
When calculating combinations, it's sometime useful to apply the following rule: nCr = nC(n-r). In other words, "n choose r" is equal to "n choose n - r"
So, for example: 10C7 = 10C3
12C9 = 12C3
8C7 = 8C1
etc.

Here's why this property works:
Let's say you have 22 friends, and you must invite 19 of them to attend your party.
This can be accomplished in 22C19 ways.
However, another way to select 19 party attendees, is to select 3 of the 22 people to NOT attend the party. Then, by default, the remaining 19 people get to attend the party.
So, selecting 3 of the 22 people to NOT attend the party is the same as selecting 19 of the 22 people TO ATTEND the party.
In other words, 22C19 = 22C3

Best of all, it's much easier to calculate 22C3 than it is to calculate 22C19

22C3 = (22)(21)(20)/(3)(2)(1)
= 1540

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### Top Member

Master | Next Rank: 500 Posts
Joined
15 Oct 2009
Posted:
325 messages
27
Brent@GMATPrepNow wrote:
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the value of 22C19?

A. 770
B. 1540
C. 3080
D. 4620
E. 6160
Best of all, it's much easier to calculate 22C3 than it is to calculate 22C19

22C3 = (22)(21)(20)/(3)(2)(1)
= 1540

Cheers,
Brent
It is ? Aren't they the same thing ?

22!/19!(22-19)! vs 22!/3!(22-3)!

Aren't we going to factor out the 19! either way ?

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12663 messages
Followed by:
1246 members
5254
GMAT Score:
770
regor60 wrote:
It is ? Aren't they the same thing ?

22!/19!(22-19)! vs 22!/3!(22-3)!

Aren't we going to factor out the 19! either way?
Good point!
I should have mentioned that I use a shortcut for calculating combinations that allows me to perform most calculations in my head.

For example, for 22C3, I write the first 3 values of 22! in the numerator, and I write the 3! in the denominator
So, 22C3 = (22)(21)(20)/(3)(2)(1)

Likewise, for 11C2, I write the first 2 values of 11! in the numerator, and I write the 2! in the denominator
So, 11C2 = (11)(10)/(2)(1) = 55

Here's a video explaining the whole technique: https://www.gmatprepnow.com/module/gmat-counting/video/789

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

GMAT Instructor
Joined
25 Apr 2015
Posted:
2012 messages
Followed by:
15 members
43
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the value of 22C19?

A. 770
B. 1540
C. 3080
D. 4620
E. 6160
22C19 is:

22!/[(22 - 19)! x 19!] = 22!/(3! x 19!) = (22 x 21 x 20)/3! = 11 x 7 x 20 = 77 x 20 = 1540

_________________
Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2038 messages
Followed by:
29 members
19
GMAT Score:
=>

Since nCn-r = nCr,
22C19 = 22C3 = (22*21*20)/(1*2*3) = 11*7*20 = 1540.

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course Free Resources-30 day online access & Diagnostic Test Unlimited Access to over 120 free video lessons-try it yourself Email to : info@mathrevolution.com • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

### Top First Responders*

1 fskilnik@GMATH 55 first replies
2 GMATGuruNY 52 first replies
3 Brent@GMATPrepNow 52 first replies
4 Jay@ManhattanReview 42 first replies
5 Rich.C@EMPOWERgma... 23 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

203 posts
2 fskilnik@GMATH

GMATH Teacher

164 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

96 posts
4 Max@Math Revolution

Math Revolution

91 posts
5 GMATGuruNY

The Princeton Review Teacher

75 posts
See More Top Beat The GMAT Experts