I need to know if I'm doing this problem accordingly

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

solution:

$\displaystyle 1-[(4)(\frac{4!}{10!}) - (4)(\frac{1}{10!}) + \frac{1}{10!}]$