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# In a garden, there are three blue flowers, three red flowers, three

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Math Expert
Joined: 02 Sep 2009
Posts: 61287
In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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06 Apr 2016, 06:03
10
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:55) correct 24% (02:10) wrong based on 205 sessions

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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

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Manager
Joined: 09 Jul 2013
Posts: 106
Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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06 Apr 2016, 08:46
1
3
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 = $$\frac{4}{220} = \frac{1}{55}$$

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.

$$\frac{2}{11}*\frac{1}{10} = \frac{1}{55}$$
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Dave de Koos
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Posts: 4329
Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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06 Apr 2016, 10:55
1
1
Bunuel wrote:
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

Related Resources
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- Probability of Event A AND Event B: https://www.gmatprepnow.com/module/gmat ... /video/750
- Rewriting Questions: https://www.gmatprepnow.com/module/gmat ... /video/754

Cheers,
Brent
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Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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12 Apr 2016, 04:50
1
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

$$\frac{(4C1*3C3)}{12C3} = \frac{1}{55}$$
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Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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27 Apr 2016, 01:05
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
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In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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03 Jul 2016, 09:21
Bunuel wrote:
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)

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Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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03 Jul 2016, 10:26
1
1
Bunuel wrote:
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
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Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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12 Jul 2017, 04:52
Bunuel wrote:
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

Intern
Joined: 14 Sep 2016
Posts: 10
Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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14 Jul 2017, 08:44
Bunuel wrote:
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.
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Joined: 09 Sep 2013
Posts: 14086
Re: In a garden, there are three blue flowers, three red flowers, three  [#permalink]

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28 Nov 2019, 23:38
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).

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Re: In a garden, there are three blue flowers, three red flowers, three   [#permalink] 28 Nov 2019, 23:38
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