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document.write( "I'm assuming you meant to have 6 twice, which means that \r\n" );
document.write( "the 4-digit number can contain 2 6's but no more than 1 of \r\n" );
document.write( "these: 0,1,2,3,4,5. [If that's not what you meant, then \r\n" );
document.write( "tell me in the thank-you form below. But I think that's\r\n" );
document.write( "what you meant].\r\n" );
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document.write( "To be divisible by 5, the last digit must either be 0 or 5. \r\n" );
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document.write( "1. First we will count all the ones allowing the first \r\n" );
document.write( " digit to be 0, but with no more than 1 6. \r\n" );
document.write( "2. Then we'll count and then subtract all those with first digit 0.\r\n" );
document.write( "3. Then we'll enumerate and add all with 2 6's, including 0665\r\n" );
document.write( "4. Then we'll subtract 1 for that single case 0665, the only one with\r\n" );
document.write( " 2 6's and first digit 0.\r\n" );
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document.write( "1. First we will count all those allowing the first \r\n" );
document.write( "digit to be 0, but with no more than 1 6. \r\n" );
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document.write( "We choose the 4th digit 2 ways. {0,5}\r\n" );
document.write( "We choose the 1st digit 6 ways.\r\n" );
document.write( "We choose the 2nd digit 5 ways. \r\n" );
document.write( "We choose the 3rd digit 4 ways.\r\n" );
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document.write( "That's 2*6*5*4 = 240 ways\r\n" );
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document.write( "2. Now we'll count (and then subtract) all those with first digit 0.\r\n" );
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document.write( "We choose the last digit 1 way, 5.\r\n" );
document.write( "We choose the 1st digit 1 way, 0.\r\n" );
document.write( "We choose the 2nd digit 5 ways.\r\n" );
document.write( "We choose the 3rd digit 4 ways.\r\n" );
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document.write( "That's 1*1*5*4 = 20 ways.\r\n" );
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document.write( "Subtracting those 20 from the 240, 240-20 = 220.\r\n" );
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document.write( "3. Now we'll enumerate and add all those with 2 6's, including 0665.\r\n" );
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document.write( "There are (3 positions, choose 2 or 3C2) ways to place the 2 6's.\r\n" );
document.write( "That's 3 ways. They are 66XY, 6X6Y, X66Y, \r\n" );
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document.write( "We can choose Y 2 ways, either 0 or 5, and then choose X 5 ways.\r\n" );
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document.write( "That's 3*2*5 = 30 ways\r\n" );
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document.write( "So we add those: 220+30 = 250\r\n" );
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document.write( "4. Now we subtract the 1 case 0665.\r\n" );
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document.write( "250-1 = 249\r\n" );
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document.write( "Answer: 249.\r\n" );
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document.write( "Edwin \n" );
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