document.write( "Question 927825: A CLUB HAS 30 FRESHMEN, 25 SOPHOMORES, 40 JUNIORS. 6 ARE CHOSEN AT RANDOM, WHATS THE PROBABILITY THAT 2 OF EACH ARE CHOSEN. \n" ); document.write( "

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$\"30%2B25%2B40=95\"$ club members.
\n" ); document.write( "From all the club members,
\n" ); document.write( " $\"95%2A94%2A93%2A92%2A91%2A90%2F%282%2A3%2A4%2A5%2A6%29\"$ different groups of 6 can be made.
\n" ); document.write( "How many of those groups include 2 freshmen, 2 sophomores and 2 juniors?
\n" ); document.write( "How many different groups of 6 can be made, including 2 freshmen, 2 sophomores and 2 juniors?
\n" ); document.write( "There are $\"30%2A29%2F2\"$ ways to choose a group of 2 freshmen out of the 30 freshmen in the club.
\n" ); document.write( "There are $\"25%2A24%2F2\"$ ways to choose a group of 2 sophomores out of the 25 sophomores in the club.
\n" ); document.write( "There are $\"40%2A39%2F2\"$ ways to choose a group of 2 juniors out of the 40 juniors in the club.
\n" ); document.write( "So, there are $\"40%2A39%2A30%2A29%2A25%2A24%2F8\"$ different groups of 6 than can be made, including 2 freshmen, 2 sophomores and 2 juniors.
\n" ); document.write( "As a fraction of all the groups of 6 that can be made, that is
\n" ); document.write( " $\"40%2A39%2A30%2A29%2A25%2A24%2A2%2A3%2A4%2A5%2A6%2F%288%2A95%2A94%2A93%2A92%2A91%2A90%29\"$ ,
\n" ); document.write( "and, as any group is as likely as any other group,
\n" ); document.write( "that is the probability that the randomly chosen group of 6 will contain exactly 2 students from each class.
\n" ); document.write( "

(rounded)
\n" ); document.write( "You could say that the probability of such a group is 11.7%. \n" ); document.write( "

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