document.write( "Question 1143366: The Gomez family and the Zhang family each have four children, two boys and two girls. At a picnic the 8 children want to form 2 teams of 4
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\n" ); document.write( " boys and 2 girls and must have 2 members of each family. In how many ways can the two teams be formed? \n" ); document.write( "
Algebra.Com's Answer #765125 by Edwin McCravy(20060)\"\" \"About 
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document.write( "I will assume that it will be OK if one family of 4 plays the other family of 4.\r\n" );
document.write( "If not we will subtract that 1 situation.  It would be much better in this type\r\n" );
document.write( "of problem if people would use definite wording like \"there are exactly 2\", or\r\n" );
document.write( "\"there are at least 2\" instead of the ambiguous \"there are 2\", which could be\r\n" );
document.write( "taken as meaning either.  [If you have 3 dollars, you have 2 dollars, right?]\r\n" );
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document.write( "Case 1:  The Gomez brothers are on the same team, and the Zhang brothers are on\r\n" );
document.write( "the other team.  \r\n" );
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document.write( "Then we have 2 boys on each team, and two from the same family on each team, so\r\n" );
document.write( "we can choose any 2 of the 4 girls to play on the Gomez brothers' team.  That's\r\n" );
document.write( "4C2 = 6 ways to choose a team for case 1, because the remaining 2 girls will\r\n" );
document.write( "play on the Zhang brothers' team, in only 1 way. \r\n" );
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document.write( "For the other two cases, notice that:\r\n" );
document.write( "One of the Gomez brothers is younger than his older brother.\r\n" );
document.write( "One of the Zhang brothers is younger than his older brother.\r\n" );
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document.write( "Case 2:  The younger Gomez boy is on the same team with the younger Zhang boy,\r\n" );
document.write( "and the older Gomez boy is on the other team with the older Zhang boy.\r\n" );
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document.write( "Then we can choose any 2 girls to play on the team with the two younger boys,\r\n" );
document.write( "because any of the 4 girls is sister to one of those boys.  So that's 4C2 = 6\r\n" );
document.write( "ways to choose a team for case 2, because the other 2 girls will play on the\r\n" );
document.write( "older boy's team.  They will both be a sister to one of the boys, making 2 from\r\n" );
document.write( "the same family on each team.  \r\n" );
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document.write( "Case 3:  The younger Gomez boy is on the same team with the older Zhang boy, and\r\n" );
document.write( "the older Gomez boy is on the other team with the younger Zhang boy.\r\n" );
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document.write( "That's just like case 2.  So that's also 4C2 = 6 ways.\r\n" );
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document.write( "Answer: 6+6+6 = 18 ways.\r\n" );
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document.write( "Edwin
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