document.write( "Question 942879: a committee of four is selected from a group of 20 people.
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Algebra.Com's Answer #575698 by Edwin McCravy(20056)\"\" \"About 
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a committee of four is selected from a group of \"cross%2820%29\"22 people.
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document.write( "Notice that I crossed out the 20 and put 22 so it would make sense.\r\n" );
document.write( " 10 women and 12 men is 22 people, not only 20 people.\r\n" );
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document.write( "The group of 4, to have a majority of men, would have either\r\n" );
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document.write( "Case 1.  3 men and 1 woman \r\n" );
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document.write( "Case 2.  4 men.\r\n" );
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document.write( "In case 1 we have 12 men CHOOSE 3, that's 12C3 = 220 ways to choose the 3\r\n" );
document.write( "men.  For each of those 20 ways, we have 10 women CHOOSE 1, that's 10C1=10.\r\n" );
document.write( "So, for case 1, there are 220×10 = 2200.\r\n" );
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document.write( "In case 2 we have 12 men CHOOSE 4, that's 12C4 = 495 ways to choose the 4\r\n" );
document.write( "men. So for case 2, there are 495.\r\n" );
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document.write( "Grand total for both cases = 2200+495 = 2695.\r\n" );
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document.write( "Edwin
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