document.write( "Question 1163313: A batch of 25 items contains 5 defective items.
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Algebra.Com's Answer #787373 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "To be \"successful\", each group consists of exactly 4 non-defective items and\r\n" );
document.write( "exactly 1 defective item.\r\n" );
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document.write( "We put 4 of the 20 non-defective items in the 1st group, 20C4 ways,\r\n" );
document.write( "then we put 4 of the remaining 16 non-defective items in the 2nd group, 16C4 ways,\r\n" );
document.write( "then we put 4 of the remaining 12 non-defective items in the 3rd group, 12C4 ways,\r\n" );
document.write( "then we put 4 of the remaining 8 non-defective items in the 4th group, 8C4 ways,\r\n" );
document.write( "then we put all 4 remaining non-defective items in the 5th group, 4C4=1 way,\r\n" );
document.write( "then\r\n" );
document.write( "we put 1 of the 5 defective items in the 1st group, 5 ways,\r\n" );
document.write( "then we put 1 of the remaining 4 defective items in the 2nd group, 4 ways\r\n" );
document.write( "then we put 1 of the remaining 3 defective items in the 3rd group, 3 ways\r\n" );
document.write( "then we put 1 of the remaining 2 defective items in the 4th group, 2 ways\r\n" );
document.write( "then we put the 1 remaining defective item in the 5th group, 1 way.\r\n" );
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document.write( "That's:\r\n" );
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document.write( "\"successful\" ways.\r\n" );
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document.write( "Now we calculate the total number of possible ways:\r\n" );
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document.write( "We put 5 of the 25 items in the 1st group, 25C5 ways,\r\n" );
document.write( "then we put 5 of the remaining 20 items in the 2nd group, 20C5 ways,\r\n" );
document.write( "then we put 5 of the remaining 15 items in the 3rd group, 15C5 ways,\r\n" );
document.write( "then we put 5 of the remaining 10 items in the 4th group, 10C5 ways,\r\n" );
document.write( "then we put all 5 remaining items in the 5th group, 5C5=1 way,\r\n" );
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document.write( "That works out to be \r\n" );
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document.write( "Edwin

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