• 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 ## Probability tagged by: BTGmoderatorRO ##### This topic has 2 expert replies and 0 member replies ## Probability Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls? A. 8/28 B. 9/28 C. 10/28 D. 10/18 E. 11/18 OA is b How can I get the correct answer to this question and which formula did you use here? Thank you so much for your response. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Roland2rule wrote: Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls? A. 8/28 B. 9/28 C. 10/28 D. 10/18 E. 11/18 OA is b How can I get the correct answer to this question and which formula did you use here? Thank you so much for your response. Total: There are 8 balls total. If we want to select 5, there are 8C5 = 8*7*6*5*4/5*4*3*2 = 56 total possible selections. Desired: We want to select 1 red ball from 2, so there's 2C1 = 2 ways to select a red ball. We want to select 2 green balls from 3, so there's 3C2 = 3 ways to select a green ball We want to select 2 blue balls from 3, so there's 3C2 = 3 ways to select a blue ball. # Desired = 2 * 3 * 3 = 18 Desired/Total = 18/56 = 9/28. The answer is B. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Apr 2015
Posted:
1465 messages
Followed by:
18 members
39
Roland2rule wrote:
Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?

A. 8/28
B. 9/28
C. 10/28
D. 10/18
E. 11/18
The number of ways to select 1 red ball is 2C1 = 2.

The number of ways to select 2 green balls is 3C2 = 3.

The number of ways to select 2 blue balls is 3C2 = 3.

So, the number of ways to select 1 red, 2 green, and 2 blue balls is 2 x 3 x 3 = 18.

The number of ways to select 5 balls from 8 is 8C5:

8!/5![(8-5)!] = 8!/(5!x3!) = (8 x 7 x 6 x 5 x 4)/5! = (8 x 7 x 6 x 5 x 4)/(5 x 4 x 3 x 2 x 1) = 7 x 2 x 4 = 56

Thus, the probability is 18/56 = 9/28.

_________________

Jeffrey Miller
jeff@targettestprep.com

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

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

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 53 first replies
2 Brent@GMATPrepNow 36 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 25 first replies
5 ceilidh.erickson 15 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

199 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

76 posts
4 Ian Stewart

GMATiX Teacher

62 posts
5 GMATGuruNY

The Princeton Review Teacher

44 posts
See More Top Beat The GMAT Experts