document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=963993>Question 963993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here's the question: <BR>\n" );
document.write( "A baseball team has 15 members. Five of the players are pitchers, and the remaining 10 members can play any position. How many different teams of 9 players can be formed?\r<BR>\n" );
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document.write( "I know this will be a Combination because order doesn't matter, but I don't know where the pitchers and normal players come in. How many pitchers are required to be on the team? <BR>\n" );
document.write( "I know that if the pitchers and normal players don't matter, the answer is simply 15C9. But do the pitchers matter? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588931 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9 players are on the field at one time.<BR>\n" );
document.write( "there is 1 pitcher, 1 catcher, 3 outfielders and 4 infielders, for a total of 9.<BR>\n" );
document.write( "i believe you have to make that assumption.<BR>\n" );
document.write( "so each team will have 1 pitcher and 8 other members on the team.\r<BR>\n" );
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document.write( "order doesn't matter.\r<BR>\n" );
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document.write( "the number of different possible 9 member teams should be:\r<BR>\n" );
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document.write( "(5c1) * (9c8) = 45.\r<BR>\n" );
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document.write( "look at this in a much smaller type problem and you can see how it works.\r<BR>\n" );
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document.write( "assume 2 pitchers and 4 other players.\r<BR>\n" );
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document.write( "assume 3 man teams of 1 pitcher and 2 other players.\r<BR>\n" );
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document.write( "number of possible teams should be 2c1 * 4c2 = 12\r<BR>\n" );
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document.write( "let the pitchers be a and b<BR>\n" );
document.write( "let the other players be 1 and 2 and 3 and 4.\r<BR>\n" );
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document.write( "the possible 3 man teams are:\r<BR>\n" );
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document.write( "a12, a13, a14, a23, a24, a34<BR>\n" );
document.write( "b12, b13, b14, b23, b24, b34\r<BR>\n" );
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document.write( "each team has 1 pitcher and 2 other players.<BR>\n" );
document.write( "each team is different.\r<BR>\n" );
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document.write( "the formula is shown to work for the smaller problem.\r<BR>\n" );
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document.write( "good chance it will work for the bigger problem.\r<BR>\n" );
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document.write( "5c1 * 9c8 = 45\r<BR>\n" );
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document.write( "5c1 = combination formula of 5! / (1! * 4!) = 5\r<BR>\n" );
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document.write( "9c8 = combination formula of 9! / (8! * 1!) = 9\r<BR>\n" );
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document.write( "5 * 9 = 45\r<BR>\n" );
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document.write( " </SPAN>\n" );
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