Last visit was: 17 Jul 2025, 12:20 It is currently 17 Jul 2025, 12:20
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
555-605 Level|   Probability|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 Jul 2025
Posts: 102,603
Own Kudos:
742,255
 [17]
Given Kudos: 98,220
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,603
Kudos: 742,255
 [17]
In a garden, there are three blue flowers, three red flowers, three 06 Apr 2016, 07:03
1
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

75% (01:49) correct 25% (02:14) wrong based on 404 sessions

History

Date
Time
Result
Not Attempted Yet
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?

A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
davedekoos
User avatar
Joined: 09 Jul 2013
Last visit: 27 Jun 2025
Posts: 96
Own Kudos:
328
 [10]
Given Kudos: 11
Posts: 96
Kudos: 328
 [10]
In a garden, there are three blue flowers, three red flowers, three 06 Apr 2016, 09:46
5
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Total number of ways to pick 3 flowers out of 12 = 12c3
\(12c3 = \frac{12!}{9!*3!} = 220\)

Total number of favorable outcomes = 4
(Only 3 flowers per colour, so there is only one way all three flowers of any particular colour can be chosen. 4 colours mean 4 favorable outcomes)

Probability = \(\frac{4}{220} = \frac{1}{55}\)

Answer: B


Alternatively, if you like the slot method, the first flower can be chosen at random, it doesn't matter. The second flower must be the same colour as the first - probability = 2/11. The third flower must be the same colour as the first two - probability = 1/10.

\(\frac{2}{11}*\frac{1}{10} = \frac{1}{55}\)
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,116
 [7]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,116
 [7]
In a garden, there are three blue flowers, three red flowers, three Updated on: 12 Oct 2021, 10:59
Originally posted by BrentGMATPrepNow on 06 Apr 2016, 11:55.
Last edited by BrentGMATPrepNow on 12 Oct 2021, 10:59, edited 1 time in total.
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Bunuel
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?

A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16

P(all the same color) = P(1st flower is ANY color AND 2nd flower is same as first AND 3rd flower is also the same color)
= P(1st flower is ANY color) x P(2nd flower is same as 1st) AND P(3rd flower is the same color)
= 1 x 2/11 x 1/10
= 1/55

Answer: B
General Discussion
User avatar
Icecream87
User avatar
Joined: 23 Sep 2015
Last visit: 02 Aug 2018
Posts: 332
Own Kudos:
343
 [5]
Given Kudos: 72
Location: France
Schools: Insead Sept '17 (M$)
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE:Real Estate (Mutual Funds and Brokerage)
Products:
My Reviews
Schools: Insead Sept '17 (M$)
GMAT 2: 700 Q48 V38
Posts: 332
Kudos: 343
 [5]
In a garden, there are three blue flowers, three red flowers, three 12 Apr 2016, 05:50
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
R: !!!
B: !!!
G: !!!
P: !!!
ways of selecting a color : 4C1
ways of selecting the three flowers within the chosen color: 3C3
ways of selecting three flowers out of 12 : 12C3

\(\frac{(4C1*3C3)}{12C3} = \frac{1}{55}\)
User avatar
AmritaSarkar89
User avatar
Joined: 22 Feb 2016
Last visit: 02 Jul 2025
Posts: 65
Own Kudos:
52
Given Kudos: 208
Location: India
Concentration: Economics, Healthcare
Schools: ISB '18 Kellogg '19 (I) Yale '19 (S) Tuck '19 (S)
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Schools: ISB '18 Kellogg '19 (I) Yale '19 (S) Tuck '19 (S)
GMAT 2: 710 Q47 V39
Posts: 65
Kudos: 52
In a garden, there are three blue flowers, three red flowers, three 27 Apr 2016, 02:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am a novice in this giving solutions but is too tempted to explain the logic of this one. Overall I have 12 flowers and I need to select just 3 of the same colour out of 12.
Let me select blue as my color
so the first flower that I pick is blue in color and I can do that in 1 way
now the second flower that I need to pick should also be blue in color so I can choose any one out of remaining two blue flowers 2/11
and finally I can choose the last blue flower in 1/10 way
So yeah
Overall P(z)= 1/55
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 21 Apr 2025
Posts: 5,965
Own Kudos:
5,160
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,965
Kudos: 5,160
In a garden, there are three blue flowers, three red flowers, three 03 Jul 2016, 10:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?

A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16

{ B B B } , { R R R } , { G G G } , { P P P } = TOTAL 12 FLOWERS

You need 3 flowers , so total no of ways it is possible is \(12c3\) = 220

Now you need one particular colour of flowers from these set...

So, We can have it in 4 ways as the sets the flowers now represents sets as below -

BLUE , RED , GREEN , PINK

\(Probability\) = \(\frac{Favourable \ Outcome}{Total \ Possible \ Outcome}\) => \(\frac{4}{220}\)

So, The answer will be (B)
User avatar
rohitrawat9990
User avatar
Joined: 20 Jan 2016
Last visit: 11 Apr 2017
Posts: 32
Own Kudos:
44
 [2]
Given Kudos: 5
GMAT 1: 600 Q47 V26
GMAT 1: 600 Q47 V26
Posts: 32
Kudos: 44
 [2]
In a garden, there are three blue flowers, three red flowers, three 03 Jul 2016, 11:26
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?

A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16



Sent from my iPhone using GMAT Club Forum mobile app
User avatar
shashankism
User avatar
Joined: 13 Mar 2017
Last visit: 23 Dec 2024
Posts: 611
Own Kudos:
670
Given Kudos: 88
Affiliations: IIT Dhanbad
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy)
Posts: 611
Kudos: 670
In a garden, there are three blue flowers, three red flowers, three 12 Jul 2017, 05:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?

A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16


Total events = 12 C 3 (i.e. selecting any 3 flowers from total 12 flowers) = 12 x 11 x 10 / 3 / 2 = 2 x 11 x 10

No. of events in which 3 flowers selected will be of same colour = 4 (3 flowers of each colour say RRR, BBB, GGG, PPP)

So required probability = 4/2/11/10 = 1/55

Answer B
avatar
goal2016
avatar
Joined: 14 Sep 2016
Last visit: 12 May 2021
Posts: 7
Own Kudos:
7
Given Kudos: 69
Posts: 7
Kudos: 7
In a garden, there are three blue flowers, three red flowers, three 14 Jul 2017, 09:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?

A. 11/10
B. 1/55
C. 31/10
D. 3/55
E. 1/16

Hi Bunuel,

Though I understood the solution, I could not get answer using this approach.
Could you help me identify the problem in this approach?

I tried like this -
3B, 3R, 3G, 3P

Now to choose 3 flowers of same colour
(3C1*2C1*1C1) * 4/12C3
I am getting 6/55

Thank you so much for help.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,439
Own Kudos:
1,013
Posts: 37,439
Kudos: 1,013
In a garden, there are three blue flowers, three red flowers, three 17 Dec 2024, 03:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
102603 posts
Krunaal
PS Forum Moderator
697 posts