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You can put this solution on YOUR website!
\r\n" ); document.write( "You didn't specify whether we may repeat digits or not.\r\n" ); document.write( "I will assume that we cannot. If we can then post again\r\n" ); document.write( "stating that digits may be repeated.\r\n" ); document.write( "\r\n" ); document.write( "Assuming digits cannot be repeated:\r\n" ); document.write( "\r\n" ); document.write( "
\n" ); document.write( "a) the numbers must be less than 500?
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document.write( "Counting 1 and 2 digit numbers;\r\n" );
document.write( "We consider 1 digit numbers as 2-digit numbers with \r\n" );
document.write( "left-most digit 0.\r\n" );
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document.write( "Choose units digit 8 ways {0,1,2,3,4,5,6,7}\r\n" );
document.write( "Choose tens digit 7 ways\r\n" );
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document.write( "That's 8*7 = 56 1 and 2 digit numbers, counting 0.\r\n" );
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document.write( "Counting three digit numbers:\r\n" );
document.write( "Choose hundreds digit 4 ways {1,2,3,4}\r\n" );
document.write( "Choose tens digit 7 ways.\r\n" );
document.write( "Choose units digit 6 ways\r\n" );
document.write( "That's 4*7*6 = 168\r\n" );
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document.write( "So that's 56+168 = 224 counting 0.\r\n" );
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document.write( "\n" ); document.write( "b) the numbers must be odd?
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document.write( "I suppose you mean it can have any number of digits up through 8 digits,\r\n" );
document.write( "since you didn't state otherwise.\r\n" );
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document.write( "7 or 8 digit numbers;\r\n" );
document.write( "(We consider 7 digit numbers as 8 digit numbers whose left-most\r\n" );
document.write( "digit is 0.)\r\n" );
document.write( "\r\n" );
document.write( "Choose units digit 4 ways {1,3,5,7}\r\n" );
document.write( "Choose tens-digit 7 ways\r\n" );
document.write( "Choose hundreds digit 6 ways\r\n" );
document.write( "Choose thousands digit 5 ways\r\n" );
document.write( "Choose ten thousands digit 4 ways\r\n" );
document.write( "Choose hundred thousands digit 3 ways\r\n" );
document.write( "Choose millions digit 2 ways\r\n" );
document.write( "Choose ten millions digit 1 way\r\n" );
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document.write( "That's 4*7*6*5*4*3*2*1 \r\n" );
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document.write( "6 or 5 digit numbers\r\n" );
document.write( "(We consider 5 digit numbers as 6 digit numbers whose left-most\r\n" );
document.write( "digit is 0.)\r\n" );
document.write( "\r\n" );
document.write( "Choose units digit 4 ways {1,3,5,7}\r\n" );
document.write( "Choose tens-digit 7 ways\r\n" );
document.write( "Choose hundreds digit 6 ways\r\n" );
document.write( "Choose thousands digit 5 ways\r\n" );
document.write( "Choose ten thousands digit 4 ways\r\n" );
document.write( "Choose hundred thousands digit 3 ways\r\n" );
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document.write( "That's 4*7*6*5*4*3\r\n" );
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document.write( "Similarly, the number of 3 or 4 digit numbers is 4*7*6*5\r\n" );
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document.write( "Similarly, the number of 1 or 2 digit numbers is 4*7 = 28\r\n" );
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document.write( "Total: 4*7*6*5*4*3*2*1 + 4*7*6*5*4*3 + 4*7*6*5 + 4*7 = 31108\r\n" );
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document.write( "c) the numbers must be even?\r\n" );
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document.write( "It's the same as (b) since there are same number even digits
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document.write( "{0,2,4,6) and there are odd digits {1,3,5,7} for the units
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document.write( "digit. Also 31108.\r
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document.write( "Edwin \n" );
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