document.write( "Question 85849: Please throughly explain how to solve this problem:\r
\n" ); document.write( "\n" ); document.write( "To win the Lotto in the state of Alabama, one must correctly select 6 numbers from a collection of 49 (1 through 49). This order in which the selection is made does not matter. How many different selections are possible?\r
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Algebra.Com's Answer #62040 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Please throughly explain how to solve this problem: \r\n" );
document.write( "To win the Lotto in the state of Alabama, one must correctly select 6 numbers\r\n" );
document.write( "from a collection of 49 (1 through 49). This order in which the selection is\r\n" );
document.write( "made does not matter. How many different selections are possible? \r\n" );
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document.write( "Checkley's answer is wrong. Since order does not matter, the answer will be \r\n" );
document.write( "the number of COMBINATIONS of 49 things taken 6 at a time:\r\n" );
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document.write( "           49·48·47·46·45·44   <-- start with 49, get 6 factors coming down)\r\n" );
document.write( "C(49,6) = ———————————————————   \r\n" );
document.write( "              1·2·3·4·5·6      <-- start with 1, get 6 factors going up\r\n" );
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document.write( "Start cancelling.  Cancel the 6 in the bottom into the 48 in the top\r\n" );
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document.write( "               8\r\n" );
document.write( "           49·48·47·46·45·44  \r\n" );
document.write( "C(49,6) = ———————————————————   \r\n" );
document.write( "              1·2·3·4·5·6    \r\n" );
document.write( "                        1\r\n" );
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document.write( "Cancel the 5 in the bottom into the 45 in the top\r\n" );
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document.write( "               8        9\r\n" );
document.write( "           49·48·47·46·45·44  \r\n" );
document.write( "C(49,6) = ———————————————————   \r\n" );
document.write( "              1·2·3·4·5·6    \r\n" );
document.write( "                      1 1\r\n" );
document.write( "  \r\n" );
document.write( "Cancel the 4 in the bottom into the 44 in the top\r\n" );
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document.write( "               8        9 11\r\n" );
document.write( "           49·48·47·46·45·44  \r\n" );
document.write( "C(49,6) = ———————————————————   \r\n" );
document.write( "              1·2·3·4·5·6    \r\n" );
document.write( "                    1 1 1\r\n" );
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document.write( "Cancel the 3 in the bottom into the 9 in the top\r\n" );
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document.write( " \r\n" );
document.write( "                        3\r\n" );
document.write( "               8        9 11\r\n" );
document.write( "           49·48·47·46·45·44  \r\n" );
document.write( "C(49,6) = ———————————————————   \r\n" );
document.write( "              1·2·3·4·5·6    \r\n" );
document.write( "                  1 1 1 1\r\n" );
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document.write( "Cancel the 2 in the bottom into the 8 in the top\r\n" );
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document.write( "               4        3\r\n" );
document.write( "               8        9 11\r\n" );
document.write( "           49·48·47·46·45·44  \r\n" );
document.write( "C(49,6) = ———————————————————   \r\n" );
document.write( "              1·2·3·4·5·6    \r\n" );
document.write( "                1 1 1 1 1\r\n" );
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document.write( "So we end up with\r\n" );
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document.write( "C(49,6) = 49·4·47·46·3·11 = 13,983,816\r\n" );
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document.write( "(So you have 1 chance out of nearly 14 million of getting them all.\r\n" );
document.write( "You can be sure the lotto creators have done this math!)\r\n" );
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document.write( "Edwin
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