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A box contains 10 pairs of shoes (20 shoes in total). If two

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Re: A box contains 10 pairs of shoes (20 shoes in total). If two  [#permalink]

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New post 19 Sep 2015, 17:10
Hi All,

In these types of questions, you'll find that there are usually at least a couple of different ways that you can 'do the math' - however, there's the potential to make everything far more complex than it needs to be. Certain Quant questions are based heavily on logic, so if you can think through the logic involved, then the math itself will be rather minimal (and sometimes quite simple).

Here, we're dealing with 10 pairs of shoes and we're asked for the probability that selecting two random shoes will lead to a matching pair.

Since there are 20 shoes in total, you will end up choosing one of them with the first 'draw.' Whichever one you choose for that first shoe, it will have a match - 1 shoe out of the remaining 19 shoes will match the first one one that you 'drew', so the probability of selecting a matching pair is 1/19.

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Re: A box contains 10 pairs of shoes (20 shoes in total). If two  [#permalink]

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New post 15 Jun 2016, 22:52
No matter what shoes you choose out of the 20 shoes,they will have an equal probability of getting selected.Now,once we have selected 1 shoe,the matching pair would be in the remaining 10 shoes and selecting them is 10c1.
So,Probability(matching shoes)=1*10c1/20c2=1/19
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Re: A box contains 10 pairs of shoes (20 shoes in total). If two  [#permalink]

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New post 04 Mar 2019, 01:42
total pairs = 10
so 1 shoe of a pair ; 1/10
P of getting another matching shoe ; 1/19
total pairs 10
1/10 * 1/19 * 10 = 1/19
IMO C

tejal777 wrote:
A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

A. 1/190
B. 1/20
C. 1/19
D. 1/10
E. 1/9


Please see my method:

Numerator:
Out of 20 shoes we have to select one shoe first..w/o any restrictions.So that's 20C1 (choosing one out of 20).
Now,the second show has to be the matching shoe.There is only ONE such possible shoe,so the probability of choosing that shoe is 1.

Denominator:
Chosing 2 shoes out of 20.So, 20C2

20C1/20C2 = 2/19

please explain:(

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Re: A box contains 10 pairs of shoes (20 shoes in total). If two   [#permalink] 04 Mar 2019, 01:42

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