document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=917936>Question 917936</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Red Sox play the Yankees in a seven game series that ends when one team has won four games.<BR>\n" );
document.write( "We record the outcome of a game with a W for a Red Sox win and an L for a Red Sox loss, e.g.<BR>\n" );
document.write( "WWWW, WLWLWLW, or WWLLLWW.<BR>\n" );
document.write( "i. How many possible outcomes are there?<BR>\n" );
document.write( "ii. How many series would have to be played to be sure that the same outcome happens twice?<BR>\n" );
document.write( "iii. If the Red Sox win in four games with a total of 17 runs, how many ways could their runs be<BR>\n" );
document.write( "distributed among the four games? (Sample run distributions: (2, 7, 5, 3) (12, 1, 1, 3))<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556844 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i. Casework on # games played (we only count # outcomes with 4 W's)\r<BR>\n" );
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document.write( "4 games: Only WWWW, 1 outcome<BR>\n" );
document.write( "5 games: Any rearrangement of WWWWL with the last game W, 4C1 = 4 outcomes<BR>\n" );
document.write( "6 games: Any rearrangement of WWWWLL, with the last game W, 5C2 = 10 outcomes<BR>\n" );
document.write( "7 games: Any rearrangement of WWWWLLL, with the last game W, 6C3 = 20 outcomes\r<BR>\n" );
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document.write( "1+4+10+20 = 35. Multiply by 2 to account for outcomes with 4 L's --> 70 different outcomes\r<BR>\n" );
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document.write( "ii. 71 by Pigeonhole\r<BR>\n" );
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document.write( "iii. Equivalent to the number of 4-tuples whose sum is 17 and each element is at least 1 (since it is impossible to win with 0 runs). This is equal to (13+3)C3 = 16C3 = 560 (look up stars and bars if you're not familiar) </SPAN>\n" );
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