document.write( "Question 436521: if a five digit number is chosen at random, what is the probability that the product of the digits is 20? \n" ); document.write( "
Algebra.Com's Answer #302054 by Edwin McCravy(20056)\"\" \"About 
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if a five digit number is chosen at ramdom, what is the probability that the product of the digits is 20?
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document.write( "Since 5 is a prime factor of 20, one of the digits must be 5\r\n" );
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document.write( "The remaining four digits must then have product 4\r\n" );
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document.write( "The only way four digits can have product 4 is for them \r\n" );
document.write( "to be 1,1,1,4 or 1,1,2,2 in some order.\r\n" );
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document.write( "The number of arrangements of 1,1,1,4 which is 4 things \r\n" );
document.write( "3 of which are indistinguishable is 4!/3! = 4\r\n" );
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document.write( "The number of arrangements of 1,1,2,2 which is 4 things \r\n" );
document.write( "2 pairs of which are indistinguishable is 4!/(2!2!) = 6\r\n" );
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document.write( "That's a total of 10 4-digit numbers which have product \r\n" );
document.write( "of digits 4.\r\n" );
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document.write( "Each of these 10 4-digit numbers have 5 places to insert \r\n" );
document.write( "a 5 to make it into a 5-digit number\r\n" );
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document.write( "[For example we can insert a 5 in \r\n" );
document.write( "the 4-digit number 2121 and make \r\n" );
document.write( "these 5 5-digit numbers 52121, 25121, 21521, 21251, 21215.)\r\n" );
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document.write( "Therefore there are 10*5 = 50 5-digit numbers with product\r\n" );
document.write( "of digits 20.\r\n" );
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document.write( "The largest 5 digit number is 99999\r\n" );
document.write( "The largest 4 digit number is 9999\r\n" );
document.write( "So there are 9999 numbers with less than 4 digits.\r\n" );
document.write( "So the number of 5-digit numbers is 99999-9999 = 90000\r\n" );
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document.write( "Therefore the desired probability is 50/90000 = 1/1800\r\n" );
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document.write( "Edwin
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