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# There are 5 pairs of shoes, all pairs are different colors.

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CEO
Joined: 15 Aug 2003
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There are 5 pairs of shoes, all pairs are different colors.  [#permalink]

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11 Sep 2003, 19:05
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There are 5 pairs of shoes, all pairs are different colors.
What is the probability that we will pick 2 shoes of same color?

check my work please.

You can pick one shoe ==> 10C1= 10 ways
The total # of ways to pick the second shoe of same color = 1
Total # of ways to pick 2 shoes out of 10 = 10C2

(10*1)/45 =2/9

thanks
praetorian

Kudos [?]: 926 [0], given: 781

CEO
Joined: 15 Aug 2003
Posts: 3452

Kudos [?]: 926 [0], given: 781

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11 Sep 2003, 19:26
MartinMag wrote:
What is the answer?

I got 1/9: 1/5*1/9*5

The author gave the answer 1/9
kindly tell me where i am wrong?

Thanks
praetorian

Kudos [?]: 926 [0], given: 781

Senior Manager
Joined: 22 May 2003
Posts: 328

Kudos [?]: 175 [0], given: 0

Location: Uruguay

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11 Sep 2003, 19:34
I like to use prob to solve these problems, but using counting methods as you did the answer would be:

Total number of pairs possible: C(10,2)=45

Of all those pairs, how many have the same color? : just 5, since from the hole lot there are not more than 2 shoes of equal color.

So 5/45=1/9

Kudos [?]: 175 [0], given: 0

CEO
Joined: 15 Aug 2003
Posts: 3452

Kudos [?]: 926 [0], given: 781

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11 Sep 2003, 20:14
MartinMag wrote:
I like to use prob to solve these problems, but using counting methods as you did the answer would be:

Total number of pairs possible: C(10,2)=45

Of all those pairs, how many have the same color? : just 5, since from the hole lot there are not more than 2 shoes of equal color.

So 5/45=1/9

I have a long way to go!
I do see how you get that...

I think I was wrong when i tried picking one by one.

Thanks
Praetorian

Kudos [?]: 926 [0], given: 781

Intern
Joined: 17 Jul 2003
Posts: 33

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12 Sep 2003, 14:08
MartinMag, can you explain it using probability, please? thanks!

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Senior Manager
Joined: 22 May 2003
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Location: Uruguay

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12 Sep 2003, 16:49
toujours28 wrote:
MartinMag, can you explain it using probability, please? thanks!

Sure...

Suppose we have colors: A,B,C,D and E

Prob of getting 1 shoe of color A=2/10=1/5

After we got the A shoe we have 9 shoes left, then the prob of getting the other A shoe is 1/9

So, probability of getting 2 shoes of color A is 1/5*1/9

Since we have 5 pairs of different colors, the answer is 1/5*1/9*5

Hope it helps!

Martin

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12 Sep 2003, 16:55
thank you very much, it makes perfect sense!
i appreciate it.

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GMAT Instructor
Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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14 Sep 2003, 03:54
MartinMag wrote:
toujours28 wrote:
MartinMag, can you explain it using probability, please? thanks!

Sure...

Suppose we have colors: A,B,C,D and E

Prob of getting 1 shoe of color A=2/10=1/5

After we got the A shoe we have 9 shoes left, then the prob of getting the other A shoe is 1/9

So, probability of getting 2 shoes of color A is 1/5*1/9

Since we have 5 pairs of different colors, the answer is 1/5*1/9*5

Hope it helps!

Martin

Here is another way of thinking about this probabilisticly.

Whatever color you pick for the first shoe, there is only one shoe out of the remaining 9 that match it, hence, the probability is 1/9.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Kudos [?]: 241 [0], given: 0

14 Sep 2003, 03:54
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# There are 5 pairs of shoes, all pairs are different colors.

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