• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

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 • 1 Hour Free 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

• 5 Day FREE Trial
Study Smarter, Not Harder

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

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

# Flor is choosing three of five colors of paint to use for he

00:00

A

B

C

D

E

## Global Stats

Difficult

Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project?

A. 7
B. 9
C. 10
D. 13
E. 17

OA A

Source: Princeton Review

### GMAT/MBA Expert

GMAT Instructor
Joined
22 Aug 2016
Posted:
1394 messages
Followed by:
26 members
470
BTGmoderatorDC wrote:
Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project?

A. 7
B. 9
C. 10
D. 13
E. 17

OA A

Source: Princeton Review
The number of ways, three out of five colors can be chosen, without any restriction = 5C3 = 5C2 = (5.4)/(1.2) = 10 ways

Out of these 10 ways, there are ways that have both Green and Yellow colors; we must exclude them.

Say, Flor chose Green and Yellow, thus, now only one color out of the three remaining colors are to be chosen.

The number of ways to choose one color out of three = 3C1 = 3 ways

Thus, the number of ways Flor can choose the colors for her project = 10 - 3 = 7 ways.

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GRE Classes Raleigh NC | GRE Prep Course Singapore | GRE Prep Philadelphia | SAT Prep Classes Toronto | and many more...

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12125 messages
Followed by:
1237 members
5254
GMAT Score:
770
BTGmoderatorDC wrote:
Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project?

A. 7
B. 9
C. 10
D. 13
E. 17
Jay's approach is the approach that I'd typically use. However, it's important to note that, when the answer choices are so small (as they are here), we should also consider the straightforward strategy of listing and counting

Let R, B, P, G and Y represent the colors Red, Blue, Purple, Green and Yellow respectively.

Now let's list the possible outcomes that meet all of the given conditions:
- RBP
- RBG
- RBY
- RPG
- RPY
- BPG
- BPY
Done!! So, there are 7 possible outcomes

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:
1466 messages
Followed by:
13 members
43
BTGmoderatorDC wrote:
Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project?

A. 7
B. 9
C. 10
D. 13
E. 17
There are three cases: 1) green is one of the five colors chosen, but yellow isn’t, 2) yellow is one of the five colors chosen, but green isn’t, and 3) neither green nor yellow is chosen. Let’s analyze each case.

Case 1: Green is one of the five colors chosen, but yellow isn’t.

If green is chosen but yellow isn’t, then we have to choose 2 more colors from the 3 remaining colors. The number of ways to do that is 3C2 = 3.

Case 2: Yellow is one of the five colors chosen, but green isn’t.
This is analogous to case 1, so there are 3 ways for this case.

Case 3: Neither green nor yellow is chosen.

If neither color is chosen, then we have to choose 3 colors from the 3 remaining colors. The number of ways to do that is 3C3 = 1.

Thus, the total number of ways Flor can choose the colors for her project is 3 + 3 + 1 = 7.

Alternate Solution:

We can use the formula:

Number of ways where yellow and green are not both included = total number of ways to pick 3 colors - number of ways where yellow and green are both included
Since we are choosing 3 colors from 5 available colors, there are 5C3 = (5 x 4)/2 = 10 ways of doing this when there are no restrictions.

The number of ways in which yellow and green are both included can be found easily by observing that yellow and green occupy two of the three slots; any one of the remaining three colors can occupy the final slot. So, there are 3 ways to choose colors where yellow and green are both included.

Thus, the number of ways to pick colors where yellow and green are not included together is 10 - 3 = 7.

_________________
Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
528 messages
Followed by:
25 members
59
BTGmoderatorDC wrote:
Flor is choosing three of five colors of paint to use for her art project at school. Two of the colors, Green and Yellow, cannot both be selected. How many different ways can Flor choose the colors for her project?

A. 7
B. 9
C. 10
D. 13
E. 17

Source: Princeton Review
RENAME colors to "unblock your brain": A, B, C, D and E.
Restriction: A and B cannot be BOTH chosen.

? = Number of choices of 3 colors among the 5 given, restriction obeyed.

First Scenario: neither A nor B is chosen.
There is just one possibility : CDE

Second Scenario: A is chosen (hence B is not)
There is just three possibilities: ACD, ACE, ADE.

Third Scenario: B is chosen (hence A is not)
This is similar to the previous scenario, hence additional 3 cases.

All cases mentioned above are MUTUALLY EXCLUSIVE, therefore they may be added: 7 possibilities.

All 7 cases are EXHAUSTIVE, hence we are sure the answer is (at least seven and) not greater than 7.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

### Top First Responders*

1 Jay@ManhattanReview 83 first replies
2 Brent@GMATPrepNow 68 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 36 first replies
5 ceilidh.erickson 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik

GMAT Teacher

199 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

160 posts
3 Scott@TargetTestPrep

Target Test Prep

109 posts
4 Jay@ManhattanReview

Manhattan Review

95 posts
5 GMATGuruNY

The Princeton Review Teacher

90 posts
See More Top Beat The GMAT Experts