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

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Bunuel
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In a garden, there are three blue flowers, three red flowers, three [#permalink] New post   06 Apr 2016, 07:03
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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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B
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davedekoos
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Re: In a garden, there are three blue flowers, three red flowers, three [#permalink] New post   06 Apr 2016, 09:46
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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.

\(\frac{2}{11}*\frac{1}{10} = \frac{1}{55}\)
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BrentGMATPrepNow
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In a garden, there are three blue flowers, three red flowers, three [#permalink] New post   Updated on: 12 Oct 2021, 10:59
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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

Answer: B

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.
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Re: In a garden, there are three blue flowers, three red flowers, three [#permalink] New post   12 Apr 2016, 05:50
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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] New post   27 Apr 2016, 02:05
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] New post   03 Jul 2016, 10:21
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] New post   03 Jul 2016, 11:26
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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] New post   12 Jul 2017, 05:52
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

Answer B
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Re: In a garden, there are three blue flowers, three red flowers, three [#permalink] New post   14 Jul 2017, 09:44
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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Re: In a garden, there are three blue flowers, three red flowers, three [#permalink] New post   06 Apr 2023, 04:25
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Re: In a garden, there are three blue flowers, three red flowers, three [#permalink]
06 Apr 2023, 04:25
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