document.write( "Question 311193: There are ten boys and twelve girls in the Leadership class. The homecoming committee has 4 members that will be picked from the lead class. What is the probability that the homecoming committee will have at least three girls?\r
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Algebra.Com's Answer #222557 by Edwin McCravy(20059) $\"\"$ $\"About$

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There are ten boys and twelve girls in the Leadership class. The homecoming committee has 4 members that will be picked from the lead class. What is the probability that the homecoming committee will have at least three girls?
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document.write( "To have a successful committee we must have \r\n" );
document.write( "3 girls AND 1 boy OR all 4 girls \r\n" );
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document.write( "The number of ways to choose 3 girls and 1 boy:\r\n" );
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document.write( "We can choose the 3 girls 12C3 ways AND the 1 boy 10C1 ways.\r\n" );
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document.write( "AND means multiply so we have (12C3)(10C1)=(220)(10)=2200 ways to choose 3 girls and 1 boy.\r\n" );
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document.write( "We can choose 4 girls and 0 boys (12C4)(10C0)=495 ways.\r\n" );
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document.write( "That's a total of 2200+495 or 2695 to successfully have 3 or 4 girls.\r\n" );
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document.write( "The total number of ways to pick any 4 from the total 22 in the lead class\r\n" );
document.write( "is 22C4 or 7315.\r\n" );
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document.write( "Therefore the probability of at least 3 girls is \r\n" );
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document.write( "That reduces by dividing numerator and denominator by 385 to\r\n" );
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document.write( "(which is about a 37% chance).\r\n" );
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document.write( "Edwin

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