document.write( "Question 849420: four random digits are drawn (repetition are allowed). Among the four digits, in how many ways can two or more repetitions occur? \n" ); document.write( "
Algebra.Com's Answer #512022 by Edwin McCravy(20055)\"\" \"About 
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document.write( "I will assume that 2922 and 7777 have more than one repetition,\r\n" );
document.write( "even though there is only one digit that is repeated.\r\n" );
document.write( "However, if these are to be considered to have only one repetition, \r\n" );
document.write( "then tell us that in the thank-you note, and we'll get back to you,\r\n" );
document.write( "and solve it that way.\r\n" );
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document.write( "The total number of ways 4 digits can be drawn is\r\n" );
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document.write( "10×10×10×10 = 104 = 10000\r\n" );
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document.write( "We will calculate the number of those that have\r\n" );
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document.write( "1. No repetitions (such as 0927)\r\n" );
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document.write( "That's 10×9×8×7 = 5040 \r\n" );
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document.write( "2. exactly 1 repetition. (such as 4575)\r\n" );
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document.write( "Choose the digit to repeat any of 10 ways\r\n" );
document.write( "Choose the 2 positions to place that repeating digit C(4,2) = 6 ways\r\n" );
document.write( "Choose a digit to place in the leftmost unfilled position 9 ways.\r\n" );
document.write( "Choose a digit to place in the rightmost unfilled position 8 ways.\r\n" );
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document.write( "That's 10×6×9×8 = 4320\r\n" );
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document.write( "So that's 5040+4320 or 9360 to subtract from 10000\r\n" );
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document.write( "10000-9360 = 640 \r\n" );
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document.write( "Answer: 640\r\n" );
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document.write( "Edwin
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