document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193874>Question 1193874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coach must reduce his basketball team from 13 players to 11 players.\r<BR>\n" );
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document.write( "Among how many different final teams has he to choose?\r<BR>\n" );
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document.write( "13C11= 13C2<BR>\n" );
document.write( "           = 13 x 12/2!<BR>\n" );
document.write( "           = 156/2<BR>\n" );
document.write( "           = 78\r<BR>\n" );
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document.write( "What is the probability that a particular player, S, will be chosen to remain on the team?\r<BR>\n" );
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document.write( "Let's say we want player S a guaranteed spot on the team. <BR>\n" );
document.write( "That leaves n = 13-1 = 12 players left to pick from and r = 11-1 = 10 slots to fill.\r<BR>\n" );
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document.write( "nCr = (n!)/(r!*(n-r)!)<BR>\n" );
document.write( "12C10 = (12!)/(10!*(12-10)!)<BR>\n" );
document.write( "12C10 = (12!)/(10!*2!)<BR>\n" );
document.write( "12C10 = (12*11*10!)/(10!*2!)<BR>\n" );
document.write( "12C10 = (12*11)/(2!)<BR>\n" );
document.write( "12C10 = (12*11)/(2*1)<BR>\n" );
document.write( "12C10 = 132/2<BR>\n" );
document.write( "12C10 = 66<BR>\n" );
document.write( "There are 66 ways to form a team where we guarantee that player S is on the team.\r<BR>\n" );
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document.write( "As you calculated correctly, 13C11 = 78 is the number of ways to select 11 players from a pool of 13. <BR>\n" );
document.write( "Among these 78 total cases, player S may or may not be on the team.\r<BR>\n" );
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document.write( "The probability player S is on the team is 66/78 = (6*11)/(6*13) = <font color=red>11/13</font><BR>\n" );
document.write( "We divide the number of ways to form a team with player S on it (66) over the number of teams total (78).<BR>\n" );
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