document.write( "Question 1153809: An organization consisting of 22 women and 16 men needs to select from its ranks a committee of 4 people.\r
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Algebra.Com's Answer #776108 by AnlytcPhil(1807) $\"\"$ $\"About$

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Ikleyn first answer is correct, but her second way is incorrect for it\r\n" );
document.write( "calculates the probability of choosing them in this order:\r\n" );
document.write( "1. any woman first from the 22 women, \r\n" );
document.write( "2. any woman second from the remaining 21 women,\r\n" );
document.write( "3. any man third from the 16 men,\r\n" );
document.write( "4. any man fourth from the remaining 15 men.\r\n" );
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document.write( "But the order in which they are chosen does not matter.\r\n" );
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document.write( "4 people with exactly 2 men also have exactly 2 women.\r\n" );
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document.write( "Choose the 2 men any of \"16 CHOOSE 2\" or 16C2 = 120 ways\r\n" );
document.write( "For each of those 120 ways to choose the 2 men, there are \r\n" );
document.write( "\"22 CHOOSE 2\" or 231 ways to choose the 2 women. That\r\n" );
document.write( "amounts to (120)(231) or 27720 ways.\r\n" );
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document.write( "The number of ways to choose ANY 4 from the 22+16=38 people is\r\n" );
document.write( "\"38 CHOOSE 4\" or 38C4 = 73815 ways.\r\n" );
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document.write( "So the probability of choosing 4 with exactly 2 men is\r\n" );
document.write( "27720 ways out of 73815 or\r\n" );
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document.write( "which reduces to\r\n" );
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document.write( "and which is approximately 37.6% of the time 2 men and 2 women\r\n" );
document.write( "will be chosen.\r\n" );
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document.write( "Edwin

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