# Probability - drawer with socks

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?

https://brainmass.com/math/probability/probability-drawer-with-socks-13698

#### 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, ...

#### Solution Summary

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