Algebra.Com's Answer #205736 by Edwin McCravy(20055)![\"\"](\"/images/stars/stars-13.gif\")  
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I am having trouble figuring this problem out.
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document.write( "What is the probability of getting a license plate that has a repeated letter or digit if the sequence is 6 letters followed by 2 numerals, followed by 1 letter (rounded to the nearest 10th. The answer I am coming up with is 76.9%, which is apparently not right. This is how I was figuring it up.
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document.write( "(25/26)(24/25)(23/24)(22/23)(21/22)(20/21)+(9/10)(8/9)+(19/20).
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document.write( "No, I'm afraid that's not correct. It should be:\r\n" );
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document.write( " .\r\n" );
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document.write( "We have to find the probability of the complement event and then subtract \r\n" );
document.write( "from 1.\r\n" );
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document.write( "The complement event is that of having NO repeated letters or digits.\r\n" );
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document.write( "A sample license plate with no repeats is, say\r\n" );
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document.write( " M Q J W U P 7 4 D\r\n" );
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document.write( "The number of possible 7-letter sequences with no repeats is \"26 position 7\",\r\n" );
document.write( "or \"26P7\". [It doesn't matter that the final D has two digits between it and\r\n" );
document.write( "the P]. And for every one of those sequences there are \"10 position 2\"\r\n" );
document.write( "sequences of 2 digits. That's 26P7*10P2.\r\n" );
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document.write( "Or. let's go through it step by step:\r\n" );
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document.write( " M Q J W U P 7 4 D\r\n" );
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document.write( "There are 26 ways to choose a letter to go where the M is. Having chosen the\r\n" );
document.write( "letter to go where the M is, \r\n" );
document.write( "there are 25 ways to choose a letter to go where the Q is. Having chosen the\r\n" );
document.write( "letters to go where the M and Q are,\r\n" );
document.write( "there are 24 ways to choose a letter to go where the J is. Having chosen the\r\n" );
document.write( "letters to go where the M, Q, and J are,\r\n" );
document.write( "there are 23 ways to choose a letter to go where the W is. Having chosen the\r\n" );
document.write( "letters to go where the M, Q, J, and A are, \r\n" );
document.write( "there are 22 ways to choose a letter to go where the U is. Having chosen the\r\n" );
document.write( "letters to go where the M, Q, J, A, and U are,\r\n" );
document.write( "there are 21 ways to choose a letter to go where the P is. Having chosen the\r\n" );
document.write( "letters to go where the M, Q, J, A, U, and P are,\r\n" );
document.write( "there are 10 ways to choose a digit to go where the 7 is. Having chosen the\r\n" );
document.write( "letters to go where the M, Q, J, A, U, P are, and a digit to go where the \r\n" );
document.write( "digit 7 is,\r\n" );
document.write( "there are 9 ways to choose a digit to go where the 4 is. Having chosen the\r\n" );
document.write( "letters to go where the M, Q, J, A, U, P are, and where the digits 7 and 4 are,\r\n" );
document.write( "there are 20 ways to choose the letter on the right end where the D is.\r\n" );
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document.write( "So there are 26*25*24*23*22*21*10*9*20 ways to choose a license plate \r\n" );
document.write( "with NO repeats.\r\n" );
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document.write( "The number of possible license plates with or without repeats is\r\n" );
document.write( "26*26*26*26*26*26*10*10*26 =  \r\n" );
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document.write( "The probability of the complement event is  .\r\n" );
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document.write( "Therefore the desired probability is\r\n" );
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document.write( " , which rounds to 0.6.\r\n" );
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document.write( "Edwin \n" );
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