document.write( "Question 917031: He chose a random positive integer factor of 10^99, what is the probability that it's also a positive integer multiple of 10^88 ? \n" ); document.write( "
Algebra.Com's Answer #556840 by Edwin McCravy(20059)\"\" \"About 
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document.write( "Since 1099 = (2*5)99 = 299599,\r\n" );
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document.write( "Every factor of of 1099 is of the form 2p5q \r\n" );
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document.write( "p and q can each be 0,1,2,...,99 which is 100 choices each.\r\n" );
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document.write( "So there are 100x100 = 10000 factors of 1099 \r\n" );
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document.write( "That's the denominator of the desired probability.\r\n" );
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document.write( "Next we calculate the numerator of the probability.\r\n" );
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document.write( "They are the positive integers of the form 2p5q\r\n" );
document.write( "which are multiples of 1088.\r\n" );
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document.write( "So p and q can can each be chosen as 88,89,90,...,99 \r\n" );
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document.write( "There are 99 integers from 1 through 99, from which we must subtract the\r\n" );
document.write( "87 integers from 1 through 87, so there are 99-87 = 12 choices for\r\n" );
document.write( "each of p and q. \r\n" );
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document.write( "So there are 12x12 = 144 factors of 1099 which are multiples of 1088.\r\n" );
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document.write( "Therefore the desired porobability is \"144%2F10000+=+9%2F625\".\r\n" );
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document.write( "Edwin
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