document.write( "Question 1163157: Your Sock drawer has six white socks, six brown socks, and for black socks. You randomly pick two socks and get a matching pair of black socks. Find the probability of this occurring. \n" ); document.write( "
Algebra.Com's Answer #787156 by greenestamps(13198)\"\" \"About 
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\n" ); document.write( "Tutor @ikleyn showed an elementary way to solve this kind of problem, by looking at the probability of picking two black socks one at a time.

\n" ); document.write( "You should know and understand that method for solving the problem.

\n" ); document.write( "For more complex problems, a more sophisticated solution method might be required. You should know that other method, demonstrated below, for solving this problem.

\n" ); document.write( "You are choosing 2 socks out of a drawer containing 16 socks. The number of ways you can do that is \"16 choose 2\": \"C%2816%2C2%29+=+%28%2816%29%2815%29%29%2F%28%282%29%281%29%29+=+120.\"

\n" ); document.write( "The outcome you want is choosing 2 of the 4 black socks. The number of ways you can do that is \"4 choose 2\": \"C%284%2C2%29+=+%28%284%29%283%29%29%2F%28%282%29%281%29%29+=+6.\"

\n" ); document.write( "The probability that you get 2 black socks is then

\n" ); document.write( "\"C%284%2C2%29%2FC%2816%2C2%29+=+6%2F120+=+1%2F20\"

\n" ); document.write( "Often, in more complicated problems, it is helpful to be more complete in describing the desired outcome. For this problem, the desired outcome is choosing 2 of the 4 black socks, AND choosing 0 of the 6 white socks, AND 0 of the 6 brown socks. Then the calculation of the probability of getting 2 black socks is

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