document.write( "Question 1041877: The access code for a car's security system consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available? \n" ); document.write( "
Algebra.Com's Answer #656833 by Edwin McCravy(20055)\"\" \"About 
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document.write( "You didn't specify whether the four digits must all be different\r\n" );
document.write( "or not.  I'll do it both ways.\r\n" );
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document.write( "If some of the digits can be the same: \r\n" );
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document.write( "choose the first digit 9 ways,   <-- {1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "choose the second digit 10 ways, <-- {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "choose the third digit 10 ways,  <-- {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "choose the fourth digit 5 ways,  <-- {0,2,4,6,8}\r\n" );
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document.write( "That's 9∙10∙10∙5 = 4500 ways, if some digits can be the same.  \r\n" );
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document.write( "If the digits must all be different, there are two cases.\r\n" );
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document.write( "Case 1.  0 comes last\r\n" );
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document.write( "choose the fourth digit 1 ways,   <-- {0}\r\n" );
document.write( "choose the first digit 9 ways, <-- {1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "choose the second digit 8 ways, <-- not the same as 4th or 1st  \r\n" );
document.write( "choose the third digit 7 ways,  <-- not the same as other three\r\n" );
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document.write( "That's 1∙9∙8∙7 = 504 ways for Case 1.\r\n" );
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document.write( "Case 2.  0 does not come last\r\n" );
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document.write( "choose the fourth digit 4 ways, <-- {2,4,6,8}\r\n" );
document.write( "choose the first digit 8 ways, <-- not 0 and not the same as 4th\r\n" );
document.write( "choose the second digit 8 ways, <-- not the same as 4th or 2nd\r\n" );
document.write( "choose the third digit 7 ways, <-- not the same as 4th\r\n" );
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document.write( "That's 4∙8∙8∙7 = 1792\r\n" );
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document.write( "Total: 504+1792 = 2296 ways, if all digits must be different.\r\n" );
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document.write( "[THING TO OBSERVE:  ALWAYS CHOOSE THE MOST RESTRICTIVE THINGS\r\n" );
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document.write( "Edwin

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