document.write( "Question 780871: How many four digit numbers can be formed from 0-9 if:
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\n" ); document.write( "the number ends in 5 and repetition is not allowed? \n" ); document.write( "
Algebra.Com's Answer #475711 by AnlytcPhil(1806)\"\" \"About 
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How many four digit numbers can be formed from 0-9 if:
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document.write( "Two ways to do that one.\r\n" );
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document.write( "First way:\r\n" );
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document.write( "Choose the 1st digit any of 9 ways.  (can't use 0)\r\n" );
document.write( "Choose the 2nd digit any of 10 ways, (can use 0)\r\n" );
document.write( "Choose the 3rd digit any of 10 ways, (can use 0)\r\n" );
document.write( "Choose the 4th digit any of 10 ways, (can use 0)\r\n" );
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document.write( "9×10×10×10 = 9000\r\n" );
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document.write( "Second way: \r\n" );
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document.write( "There are 9999 positive integers from 1 thru 9999 inclusively.\r\n" );
document.write( "Of those the 999 integers from 1 through 999 inclusively are \r\n" );
document.write( "not four-digit numbers.  So there are 9999-999 = 9000 \r\n" );
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\n" ); document.write( "the number is less than 5000 and repetitions are allowed?
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document.write( "Choose the 1st digit any of 4 ways, (1,2,3,or 4)\r\n" );
document.write( "Choose the 2nd digit any of 10 ways.\r\n" );
document.write( "Choose the 3rd digit any of 10 ways.\r\n" );
document.write( "Choose the 4th digit any of 10 ways.\r\n" );
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document.write( "Answer: 4×10×10×10 = 4×103 = 4000\r\n" );
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document.write( "Second way: \r\n" );
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document.write( "There are 4999 positive integers less than 5000.\r\n" );
document.write( "Of those the 999 integers from 1 through 999 inclusively are \r\n" );
document.write( "not four-digit numbers.  So there are 4999-999 = 4000 \r\n" );
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\n" ); document.write( "the number is less than 5000 and no repetitions are allowed?
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document.write( "Choose the first digit first as that is the most restrictive.\r\n" );
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document.write( "Choose the 1st digit any of the 4 ways (as 1,2,3,or 4\r\n" );
document.write( "Choose the 2nd digit in any of the 9 remaining ways.\r\n" );
document.write( "Choose the 3rd digit in any of the 8 remaining ways.\r\n" );
document.write( "Choose the 4th digit in any of the 7 remaining ways.\r\n" );
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document.write( "Answer:  4×9×8×7 = 2016 ways \r\n" );
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\n" ); document.write( "the number ends in 5 and repetition is allowed?
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document.write( "First way:\r\n" );
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document.write( "Choose the 4th digit only 1 way, as 5.\r\n" );
document.write( "Choose the 1st digit any of 9 ways.  (can't use 0)\r\n" );
document.write( "Choose the 2nd digit any of 10 ways, (can use 0)\r\n" );
document.write( "Choose the 3rd digit any of 10 ways, (can use 0)\r\n" );
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document.write( "1×9×10×10 = 900\r\n" );
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document.write( "Second way:\r\n" );
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document.write( "Choose the 3-digit number that precedes the 5. \r\n" );
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document.write( "There are 999 positive integers from 1 thru 999 inclusively.\r\n" );
document.write( "Of those the 999 integers from 1 through 99 inclusively are \r\n" );
document.write( "not three-digit numbers.  So there are 999-99 = 900 3-digit\r\n" );
document.write( "numbers that you can put a 5 on the right end as a 4th digit\r\n" );
document.write( "ending in 5.  Answer: 900\r\n" );
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\n" ); document.write( "the number ends in 5 and repetition is not allowed?
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document.write( "Choose the last digit first as that is the most restrictive.\r\n" );
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document.write( "Choose the 4th digit only 1 way, as 5.\r\n" );
document.write( "Choose the 1st digit any of 8 remaining ways.  (can't use 0 or 5)\r\n" );
document.write( "Choose the 2nd digit any of 8 remaining ways, (can use 0, but not 5)\r\n" );
document.write( "Choose the 3rd digit any of 7 ways.\r\n" );
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document.write( "1×8×8×7\r\n" );
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document.write( "Answer:  1×8×8×7 = 448 ways \r\n" );
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document.write( "Edwin
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