document.write( "Question 325397: Please help\r
\n" ); document.write( "\n" ); document.write( "How many 5 letter passwords can be formed from the letters PAYMENT if no repetition of letters is allowed?\r
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Algebra.Com's Answer #233017 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "You can choose the first letter as any of the 7 letters in the word.  \r\n" );
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document.write( "For each of those 7 ways to choose the 1st letter, you can choose the 2nd\r\n" );
document.write( "letter as any of the 6 remaining letters which weren't chosen for the first\r\n" );
document.write( "letter.  That's 7*6 ways to choose the first 2 letters.\r\n" );
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document.write( "For each of those 7*6 ways to choose the 1st 2 letters, you can choose the 3rd\r\n" );
document.write( "letter as any of the 5 remaining letters which weren't chosen for either of the\r\n" );
document.write( "first 2 letters.  That's 7*6*5 ways to choose the first 3 letters.\r\n" );
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document.write( "For each of those 7*6*5 ways to choose the 1st 3 letters, you can choose the 4th\r\n" );
document.write( "letter as any of the 4 remaining letters which weren't chosen for any the first\r\n" );
document.write( "3 letters.  That's 7*6*5*4 ways to choose the first 4 letters.\r\n" );
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document.write( "For each of those 7*6*5*4 ways to choose the 1st 4 letters, you can choose the\r\n" );
document.write( "5th, or last letter as any of the 3 remaining letters which weren't chosen for\r\n" );
document.write( "any the first 4 letters.  That's 7*6*5*4*3 ways to choose the 5 letters.\r\n" );
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document.write( "Answer 7*6*5*4*3 = 2520 possible 5-letter passwords.\r\n" );
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document.write( "This can also be written 7P5 and the formula is\r\n" );
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document.write( "OR if you prefer\r\n" );
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document.write( " --> (R factors)\r\n" );
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document.write( " --> (5 factors) = 2520.\r\n" );
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document.write( "Edwin

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