document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164030>Question 1164030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? </SPAN>\n" );
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document.write( "The question \"how many vote totals are there\" is ambiguous.<br><BR>\n" );
document.write( "With one interpretation, since there are 50 people voting, there is only one \"vote total\" possible: 50.<br><BR>\n" );
document.write( "With the interpretation from the other tutor who has responded, the number of possible vote totals is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E50 ALIGN=MIDDLE  ALT=\"4%5E50\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since each of the 50 people has 4 choices of whom to vote for.<br><BR>\n" );
document.write( "I have a different interpretation: the number of ways the 50 votes can be distributed among the 4 candidates.<br><BR>\n" );
document.write( "Using \"stars and bars\" (search this site, or the internet in general, if you aren't familiar with that), the number of ways is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2850%2B3%2C3%29+=+C%2853%2C3%29 ALIGN=MIDDLE  ALT=\"C%2850%2B3%2C3%29+=+C%2853%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 23426}<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );