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# Probability - drawer with socks

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1) A drawer contains n=5 different and distinguishable pairs of socks
(a total of 10 socks). If a person randomly selects 4 socks, what is
the probability that there is no matching pair in the sample?

2) A drawer contains n different and distinguishable pairs of socks (a
total of 2n socks). A person randomly selects 2r of the socks, where
2r > n. In terms of n and r, what is the probability that there is no
matching pair in the sample?

##### Solution Summary

There are two probability questions regarding a drawer with socks of different colors here.

##### Solution Preview

1) These socks are distinct, so the order of choice is important. The total possible choices are: 10*9*8*7, i.e. we have ten options first, then 9 for the second choice and so on.
The possible desired methods are 10*8*6*4, i.e. again we can choose any one of them, ...

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