document.write( "Question 890885: A United States Delegation consists of 6 Americans, 5 Russians, and 4 Chinese. How many committees of three people have more Americans than Russians?
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Algebra.Com's Answer #539454 by Edwin McCravy(20055)\"\" \"About 
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A United States Delegation consists of 6 Americans, 5 Russians, and 4 Chinese.
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document.write( "Case 1:  1 American, 0 Russians, 2 Chinese\r\n" );
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document.write( "6 Americans choose 1, C(6,1) = 6\r\n" );
document.write( "5 Russians choose 0, C(5,0) = 1\r\n" );
document.write( "4 Chinese choose 2, C(4,2) = 6\r\n" );
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document.write( "6󪻖 = 36 ways\r\n" );
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document.write( "Case 2:  2 Americans, 0 Russians, 1 Chinese\r\n" );
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document.write( "6 Americans choose 2, C(6,2) = 15\r\n" );
document.write( "5 Russians choose 0, C(5,0) = 1\r\n" );
document.write( "4 Chinese choose 1, C(4,1) = 4\r\n" );
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document.write( "15󪻔 = 60 ways\r\n" );
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document.write( "Case 3:  2 Americans, 1 Russian, 0 Chinese\r\n" );
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document.write( "6 Americans choose 2, C(6,2) = 15\r\n" );
document.write( "5 Russians choose 1, C(5,1) = 5\r\n" );
document.write( "4 Chinese choose 0, C(4,0) = 1\r\n" );
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document.write( "15󬊁 = 75 ways\r\n" );
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document.write( "Case 4:  3 Americans, 0 Russians, 0 Chinese\r\n" );
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document.write( "3 Americans choose 2, C(6,3) = 20\r\n" );
document.write( "0 Russians choose 1, C(5,1) = 1\r\n" );
document.write( "0 Chinese choose 0, C(4,0) = 1\r\n" );
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document.write( "20󪻑 = 20 ways\r\n" );
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document.write( "Answer: 36+60+75+20 = 191 committees with more Ameericans than Russaians.\r\n" );
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document.write( "First we calculate the number of possible committees of three people.\r\n" );
document.write( "There are 6+5+4 = 15 people\r\n" );
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document.write( "15 people choose 3 = C(15,3) = 455 committees\r\n" );
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document.write( "From that we subtract the number of all American committees.\r\n" );
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document.write( "6 Americans choose 3 = C(6,3) = 20\r\n" );
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document.write( "Answer = 455 - 20 = 435\r\n" );
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document.write( "Edwin
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