document.write( "Question 908836: Can you please help me with this?\r
\n" ); document.write( "\n" ); document.write( "A modern Master combination lock is electronic and the combination consists of a series of up, down, left, and right clicks. The user-created combination can vary from 4-12 clicks. Again, order is important, and repetition is allowed. How many combinations are possible with a 4-click combination?\r
\n" ); document.write( "\n" ); document.write( "P = (n*4)r = (12*4)4 = 484 = 5,308,416 is what I tried. \n" ); document.write( "
Algebra.Com's Answer #551404 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "[By the way, the word \"combination\" when used to refer to a combination\r\n" );
document.write( "lock has nothing to do with the idea of \"combinations\" in math courses.]  \r\n" );
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document.write( "If I'm interpreting your problem correctly, you might have a \r\n" );
document.write( "lock combination of:\r\n" );
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document.write( "4 clicks, for instance Up,Down.Down,Right, abbreviated UDDR.\r\n" );
document.write( "There would be 4*4*4*4 or 44 such lock combinations.\r\n" );
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document.write( "Or you might have a lock combination with 5 clicks, for instance, \r\n" );
document.write( "Left, Left, Right, Down, UP, abbreviated LLRDU,\r\n" );
document.write( "There would be 4*4*4*4*4 or 45 such lock combinations.\r\n" );
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document.write( "or you might have a lock combination with any number of clicks up\r\n" );
document.write( "to and including 12 clicks.  For instance if you had a lock \r\n" );
document.write( "combination with 12 clicks, it  might be DDRRRULRLLUU.\r\n" );
document.write( "There would be 412 such lock combinations.\r\n" );
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document.write( "Since there are 4 clicks, if you have a string on n clicks there \r\n" );
document.write( "would be 4*4*4*...*4 to n factors or 4n possible \r\n" );
document.write( "combinations consisting of n clicks..\r\n" );
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document.write( "Therefore the total number of lock combinations would be \r\n" );
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document.write( "44+45+46+47+48+49+410+411+412\r\n" );
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document.write( "which is the sum of a geometric series with \"a%5B1%5D=4%5E4\", \"a%5Bn%5D=4%5E12\", and \"r=4\"\r\n" );
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document.write( "A formula for the sum of a geometric series is\r\n" );
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document.write( "\"S=%28r%2Aa%5Bn%5D-a%5B1%5D%29%2F%28r-1%29=%284%2A4%5E12-4%5E4%29%2F%284-1%29=22369536\"\r\n" );
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document.write( "Edwin
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