document.write( "Question 1164030: A certain club has $50$ people, and $4$ members are running for president. Each club member votes for one of the $4$ candidates. How many different possible vote totals are there? \n" ); document.write( "

Algebra.Com's Answer #788329 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Every one of 50 club members, can vote for any of 4 candidates.\r\n" );
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document.write( "The total number of all possible different votes is, therefore, .\r\n" );
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document.write( "    To make this result more clear, you may think this way.\r\n" );
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document.write( "You write the protocols of voting.\r\n" );
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document.write( "In the row of 50 positions, you write the first letters of the names of 4 candidates A, B, C or D, in each position.\r\n" );
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document.write( "Thus you get the \"word\" of the length of 50 letters, written in this 4-symbols alphabet {A,B,C,D}.\r\n" );
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document.write( "In the 1-st  position, you may have any of 4 letters;\r\n" );
document.write( "In the 2-nd position, you may have any of 4 letters, again, independently;\r\n" );
document.write( "In the 3-rd position, you may have any of 4 letters, again, independently;\r\n" );
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document.write( "   . . .  and so on  till 50-th position.\r\n" );
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document.write( "In this way, you get a huge set of all possible different protocols - all possible voting  results.\r\n" );
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document.write( "The problem asks about the number of all such possible protocols,\r\n" );
document.write( "which is the number of all possible 50-letter words, written in 4-symbol alphabet {A,B,C,D}.\r\n" );
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document.write( "In this way, you get the number  ,  which is your   ANSWER\r\n" );
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