document.write( "Question 143040: A bag contains 15 billiard balls, numbers consecutively from 1 to 15. Six balls are selected at random. What is the probability that the sum of the numbers on the billiard balls will be odd? \n" ); document.write( "
Algebra.Com's Answer #104093 by Edwin McCravy(20060)\"\" \"About 
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document.write( "The 7 even numbered balls are 2,4,6,8,10,12,14\r\n" );
document.write( "The 8 odd numbered balls are  1,3,5,7,9,11,13,15.\r\n" );
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document.write( "There will be an odd sum is there is an odd number of\r\n" );
document.write( "odd numbered balls, and an even sum if there is an even\r\n" );
document.write( "number of odd balls.  So the cases of an odd number of\r\n" );
document.write( "odd numbered balls:\r\n" );
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document.write( "N(1 odd numbered ball & 5 even numbered balls) = C(8,1)*C(7,5) = 8*21  =  168\r\n" );
document.write( "N(3 odd numbered ball & 3 even numbered balls) = C(8,3)*C(7,3) = 56*35 = 1960\r\n" );
document.write( "N(5 odd numbered ball & 1 even numbered balls) = C(8,5)*C(7,1) = 56*7  =  392\r\n" );
document.write( "                                                                 Total = 2520\r\n" );
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document.write( "The total number of choices of any 6 balls out of the 15 is C(15,6) = 5005  \r\n" );
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document.write( "So the desired probability = 2520/5005 = 72/143\r\n" );
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document.write( "Edwin
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