SOLUTION: Of 10 girls in a class, three have blue eyes. Two of the girls are chosen at random. Find the probability that exactly one has blue eyes.

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Question 1119077: Of 10 girls in a class, three have blue eyes. Two of the girls are chosen at random. Find the probability that exactly one has blue eyes.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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To solve this problem, you need to answer 2 questions:



1.  How many pairs of girls can be formed of 10 girls ?

    The answer is  C%5B10%5D%5E2 = %2810%2A9%29%2F2 = 45 pairs.



2.  How many pairs are there where exactly one girl has blue eyes ?


    You may choose first blue-eyed girl and add any other of 7 remaining non-blue-eyed girls: 7 options in all.


    You can do the same with the other and the third blue-eyed girl.

    In this way you will get  7 + 7 + 7 = 21 pairs of girls, where only one girl is blue eyed.



3.  Now you can easily answer the problem question:

        the probability under the question is  21%2F45 = 7%2F15.