document.write( "Question 1202550: A class of 10 boys and 10 girls a committee of 5 are choosen. What is the probability that all are of the same sex? \n" ); document.write( "

Algebra.Com's Answer #837466 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Here are two basic ways of solving this problem.

\n" ); document.write( "(1) Using the basic definition of probability

\n" ); document.write( "The good outcomes are either selecting 5 of the 10 boys or 5 of the 10 girls; the possible outcomes are selecting 5 of the 20 students.

\n" ); document.write( " $\"P=%28C%2810%2C5%29%2BC%2810%2C5%29%29%2FC%2820%2C5%29\"$

\n" ); document.write( " $\"P=%28252%2B252%29%2F%2815504%29=21%2F646\"$

\n" ); document.write( "(2) Choosing one student at a time and multiplying the probabilities that the desired outcome is obtained. The first student chosen can be any of the 20 students; after that, the next four students chosen must be the same sex as the first.

\n" ); document.write( " $\"P=%2820%2F20%29%289%2F19%29%288%2F18%29%287%2F17%29%286%2F16%29=3024%2F93024=21%2F646\"$

\n" ); document.write( "ANSWER: 21/646

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