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

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Intern
Joined: 04 Nov 2005
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A florist has 2 azaleas, 3 buttercups, and 4 petunias. She [#permalink]  06 Nov 2005, 22:39
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 doesn't want two of the same flower. What is the probability that the florist doesn't have to change the bouquet.

Thanks in advance for the help.
Director
Joined: 14 Sep 2005
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Location: South Korea
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Kudos [?]: 13 [0], given: 0

Total flowers : AA, BBB, PPPP

Probability that two same flowers are picked:

AA = 2/9 * 1/8 = 1/36
BB = 3/9 * 2/8 = 1/12
PP = 4/9 * 3/8 = 1/6
--------------------------
1/36 + 1/12 + 1/6 = 5/18

1 - 5/18 = 13/18

Thus, 13/18
_________________

Auge um Auge, Zahn um Zahn !

VP
Joined: 22 Aug 2005
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gamjatang wrote:
Total flowers : AA, BBB, PPPP

Probability that two same flowers are picked:

AA = 2/9 * 1/8 = 1/36
BB = 3/9 * 2/8 = 1/12
PP = 4/9 * 3/8 = 1/6
--------------------------
1/36 + 1/12 + 1/6 = 5/18

1 - 5/18 = 13/18

Thus, 13/18

gamjatang, does it make a difference if she picks "2 flowers together"?
your explanation seems picking 2 one after other
. Just a thought, I am not able to find out, the different way though.
Intern
Joined: 04 Nov 2005
Posts: 2
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gamjatang wrote:
Total flowers : AA, BBB, PPPP

Probability that two same flowers are picked:

AA = 2/9 * 1/8 = 1/36
BB = 3/9 * 2/8 = 1/12
PP = 4/9 * 3/8 = 1/6
--------------------------
1/36 + 1/12 + 1/6 = 5/18

1 - 5/18 = 13/18

Thus, 13/18

Thanks for the help. 13/18 is the answer in the book but I cant see how to get to it.

Where do you get the "*1/8" "*2/8" "*3/8"
Director
Joined: 14 Sep 2005
Posts: 998
Location: South Korea
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Kudos [?]: 13 [0], given: 0

cjrylant wrote:
gamjatang wrote:
Total flowers : AA, BBB, PPPP

Probability that two same flowers are picked:

AA = 2/9 * 1/8 = 1/36
BB = 3/9 * 2/8 = 1/12
PP = 4/9 * 3/8 = 1/6
--------------------------
1/36 + 1/12 + 1/6 = 5/18

1 - 5/18 = 13/18

Thus, 13/18

Thanks for the help. 13/18 is the answer in the book but I cant see how to get to it.

Where do you get the "*1/8" "*2/8" "*3/8"

// cjrylant

There are 9 flowers now.

After you pick one, then there are 8 flowers left.

Likewise, there are 4 PPPP now.

After you pick one P, then there are three PPP left.

That's where "1/8", "2/8", and "3/8" came from.

// duttsit

If you pick two flowers at one time, the result will be the same.
The formula will be like following (and is much more time-consuming);

1) Total number of possible picks
= 9C2 = 9*8/2=36

2) Possible number of cases in which two A's are picked
= 2C2 = 1

2) Possible number of cases in which two B's are picked
= 3C2 = 3

3) Possible number of cases in which two P's are picked
= 4C2 = 6

-----------------------------------------------------------------

From 1), 2), 3), and 4), we can see that the possibility of picking two same flowers is (1+3+6)/36 = 10/36 = 5/18

Thus, the possibility of picking two different flowers is 1 - 5/18 = 13/18.
_________________

Auge um Auge, Zahn um Zahn !

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