SOLUTION: A drawer contains 4 red, 5 blue, and 5 white socks. Three socks are removed from the drawer without looking. a.What is the probability that the three socks selected do not contain

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Question 922366: A drawer contains 4 red, 5 blue, and 5 white socks. Three socks are removed from the drawer without looking.
a.What is the probability that the three socks selected do not contain a matching pair?
b.What is the probability of getting a matching pair among the three drawn socks?
c.Suppose four socks are taken from the drawer, What is the probability of not getting a matching pair?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
a.What is the probability that the three socks selected do not contain a
matching pair?
That means she got one of each color.
She could have selected the red one any of 4 ways, the blue one any of 5 
ways, and the white one any of 5 ways.  That's 4*5*5 = 100 ways.

That's the numerator of the probability.

The denominator is 14C3 = 364.  So the probability that she did not get
a matching pair is 100%2F364=25%2F91 or about 27.5% of the time.  

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b.What is the probability of getting a matching pair among the three drawn
socks?
1 - the probability of getting one of each color = 1-25%2F91=66%2F91 
or about 72.5% of the time. 

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c.Suppose four socks are taken from the drawer, What is the probability of not
getting a matching pair?
That's a trick question.  The answer is 0, because there are only 3 colors and
it is therefore impossible to get 4 different colors.  :)

Edwin