document.write( "Question 1104728: A meeting takes place between a diplomat and seventeen government officials. However, ten of the officials are actually spies. If the diplomat gives secret information to eight of the attendees, what is the probability that the diplomat gave secret information to exactly five spies? \n" ); document.write( "

Algebra.Com's Answer #720218 by ikleyn(52925) $\"\"$ $\"About$

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document.write( "Among 17 government officials there are 10 spies and 7 loyal officials, according to the condition.\r\n" );
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document.write( "So, to answer the problem's question, you actually should answer two questions:\r\n" );
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document.write( "        1.  In how many ways the groups of the 8 attendees can be formed of 17 officials ?\r\n" );
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document.write( "    and\r\n" );
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document.write( "        2.  In how many ways the groups of the 8 attendees can be formed of 17 officials under the condition that each such group \r\n" );
document.write( "            contains exactly 5 spies and 3 loyal diplomats ?\r\n" );
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document.write( "The answer to question #1 is:  in  =  = 24310 ways.\r\n" );
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document.write( "    It is the cardinality of the full space of events.\r\n" );
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document.write( "The answer to question #2 is:  in  . = * = 252*35 = 8820 ways.\r\n" );
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document.write( "And now the final answer is:  The probability under the problem's question is  = 0.3628 (approximately).\r\n" );
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