document.write( "Question 264379: A pin code is a sequence of three numbers, each of which is between 1 and 9. If none of the numbers in the sequence can repeat, how many combinations for the code are possible? \n" ); document.write( "

Algebra.Com's Answer #194643 by Edwin McCravy(20055) $\"\"$ $\"About$

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pin code is a sequence of three numbers, each of which is between 1 and 9. If none of the numbers in the sequence can repeat, how many combinations for the code are possible?
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document.write( "I'm not sure what you mean by \"between\" -- inclusive or exclusive? \r\n" );
document.write( "1 and 9 are not \"between\" 1 and 9, Do you mean including 1 and 9 \r\n" );
document.write( "or just the seven numbers 2,3,4,5,6,7, and 8?\r\n" );
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document.write( "If you are including 1 and 9, then,\r\n" );
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document.write( "Choose the first number any of 9 ways.\r\n" );
document.write( "For ever one of those 9 ways to choose the first number, \r\n" );
document.write( "there are 8 ways left to choose the second number,\r\n" );
document.write( "So that 9*8 or 72 ways to choose the first two numbers.\r\n" );
document.write( "For each of those 72 ways to choose the first two numbers,\r\n" );
document.write( "there are 7 ways left to choose the third number, so that's\r\n" );
document.write( "9*8*7 or 72*7 or 504 ways.\r\n" );
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document.write( "If you are NOT including 1 and 9, but only the 7 numbers in\r\n" );
document.write( "between 1 and 9, that is, 2,3,4,5,6,7,and 8 then,\r\n" );
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document.write( "Choose the first number any of 7 ways.\r\n" );
document.write( "For ever one of those 7 ways to choose the first number, \r\n" );
document.write( "there are 6 ways left to choose the second number,\r\n" );
document.write( "So that 7*6 or 42 ways to choose the first two numbers.\r\n" );
document.write( "For each of those 42 ways to choose the first two numbers,\r\n" );
document.write( "there are 5 ways left to choose the third number, so that's\r\n" );
document.write( "7*6*5 or 42*5 or 210 ways.\r\n" );
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document.write( "So, the answer is either 504 or 210 depending on what you mean\r\n" );
document.write( "by \"between 1 and 9\"\r\n" );
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document.write( "Edwin

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