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A florist has 2 azaleas, 3 buttercups, and 4 petunias. She

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A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?

A. 5/18
B. 13/18
C. 1/9
D. 1/6
E. 2/9
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Nov 2012, 05:36, edited 1 time in total.
Renamed the topic and edited the question.
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ajit257 wrote:
A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts 2 flowers together at random in a bouquet. However customer calls and says she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet ?


Let's count the probability of the opposite event and subtract it from 1. Opposite event would be that the florist made a bouquet with two of the same flower: \(\frac{C^2_2+C^2_3+C^2_4}{C^2_{9}}=\frac{10}{36}\) --> \(P=1-\frac{10}{36}=\frac{26}{36}=\frac{13}{18}\)

Answer: B.
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total possibilities of selecting 2 flowers from 9 = 9*8= 72
position doesn't matter i.e. {AB} & {BA} mean the same. so total cases = \(\frac{72}{2} = 36\)

total cases where both flowers are same.

{AA} = 2*1= 2
{BB} = 3*2= 6
{PP} = 4*3= 12
= 2+6+12= 20

position doesn't matter. so total cases \(= \frac{20}{2} = 10\)

Ans \(= 1 - \frac{10}{36} = \frac{13}{18}\)

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Pls help with explanation for this problem from MGMAT Strategy Guide 5 [#permalink]

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What we have: 2A, 3B, 4P
Total: 9 flowers

Prob of selecting 2A: (2/9)(1/8)=1/36
Prob of selecting 2B: (3/9)(2/8)=1/12=3/36
Prob of selecting 2P: (4/9)(3/8)=1/6=6/36

1/36+3/36+6/36=10/36=5/18

1-(5/18)=13/18
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arpshriv wrote:
A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together
at random in a bouquet. However, the customer calls and says that she does not
want two of the same flower. What is the probability that the florist does not have to
change the bouquet?


Merging similar tropics. please refer to the discussion above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1,3, 7 and 8. Thank you.


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Re: Probability ..tough one [#permalink]

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New post 05 Feb 2011, 10:37
##2 azaleas(A), 3 buttercups(B), and 4 petunias(P)##

To select two flowers, each from a different type is:
1A and 1P
or
1B and 1P
or
1A and 1B

We can select 1A from 2 in \(C^2_1\) ways
We can select 1B from 3 in \(C^3_1\) ways
We can select 1P from 4 in \(C^4_1\) ways

P(2 flowers, each of different type) is

\(\frac{C^2_1*C^3_1+C^2_1*C^4_1+C^3_1*C^4_1}{C^9_2}\)

\(\frac{2*3+2*4+3*4}{9*4}\)

\(\frac{6+8+12}{36}\)

\(\frac{26}{36}\)

Ans: \(\frac{13}{18}\)
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Florist 2azaleas, 3 buttercups and 4 petunias [#permalink]

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New post 16 Nov 2012, 20:19
dimri10 wrote:
2 azaleas, 3 buttercups, and 4 petunias for total of 9:
same flower:
2 azaleas- 2/9*1/8 of choosing the same flower.
3 buttercups- 3/9*2/8
4 petunias - 4/9*3/8
2/72+6/72+12/72=20/72 Probability to chhose the same flower.

we want the probability of not choosing so 1-20/72=52/72=26/36=13/18



Would someone please explain why do we multiply by 1/8, 2/8, 3/8?
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A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts... [#permalink]

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New post 02 Sep 2015, 09:49
A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?

Answer:

1. Counting manually (by drawing a table) all possible combinations of bouquets with two same flowes
2. Counting all possible combinations of two flower bouquets by using anagram grid
3. Making probability fraction of amount of possible bouquets with 2 same flowers to all possible bouquets (two same flower and two different flower bouquets)
4. Subtracting upper probability fraction (something we have to exclude) from 1.

The answer is 13/18

[Reveal] Spoiler:
I don't understand the solution method being used here. I translated the question being asked as "what is the probability that the first two flower bouquet that the florist picked was NOT a bouquet of two same flowers, meaning what is the probability that the first two flower bouquet that the florist picked was either AB OR BP OR AP?". Basically I used probability tree to solve this but I got different answer : 13/36.

AB = One flower is Azalea AND second flower is Buttercup
2/9 x 3/8 = 1/12

OR

BP = one flower is buttercup and second is petunia
3/9 x 4/8 = 1/6

OR

AP = one flower is azalea and second is petunia
2/9 x 4/8 = 1/9

Final answer = 1/12 + 1/6 + 1/9 = 13/36

How is my thinking wrong?
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New post 02 Sep 2015, 09:56
Expert's post
MariaVorop wrote:
A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?

Answer:

1. Counting manually (by drawing a table) all possible combinations of bouquets with two same flowes
2. Counting all possible combinations of two flower bouquets by using anagram grid
3. Making probability fraction of amount of possible bouquets with 2 same flowers to all possible bouquets (two same flower and two different flower bouquets)
4. Subtracting upper probability fraction (something we have to exclude) from 1.

The answer is 13/18

[Reveal] Spoiler:
I don't understand the solution method being used here. I translated the question being asked as "what is the probability that the first two flower bouquet that the florist picked was NOT a bouquet of two same flowers, meaning what is the probability that the first two flower bouquet that the florist picked was either AB OR BP OR AP?". Basically I used probability tree to solve this but I got different answer : 13/36.

AB = One flower is Azalea AND second flower is Buttercup
2/9 x 3/8 = 1/12

OR

BP = one flower is buttercup and second is petunia
3/9 x 4/8 = 1/6

OR

AP = one flower is azalea and second is petunia
2/9 x 4/8 = 1/9

Final answer = 1/12 + 1/6 + 1/9 = 13/36

How is my thinking wrong?


Merging similar tropics. Please refer to the discussion above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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A florist has 2 azaleas, 3 buttercups, and 4 petunias. She [#permalink]

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New post 18 Sep 2015, 03:58
Hi All,
,

This also one way to solve this, it takes maybe slightly longer. This approach is not efficient when dealing with larger "cases".

Azaleas = A
Buttercups = B
Petunias = B

Recap: For the florist to not change the bouquet, different flowers would have been picked.
So, We need to find the probability of three different cases.
P(AB)+P(AP) + P(BP).

P(AB) = 2/9 * 3/8 = 6/72
P(AP) = 2/9 * 4/8 = 8/72
P(BP) = 4/9 * 3/8 = 12/72

Now in each case, we have two different outcomes (AB + BA)

2*(6/72+ 8/72+12/72) = 52/72 = 13/18
A florist has 2 azaleas, 3 buttercups, and 4 petunias. She   [#permalink] 18 Sep 2015, 03:58
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