document.write( "Question 735802: Here is the problem: A soccer team has 16 players. How many ways can the coach choose a starting team of 11 players?\r
\n" ); document.write( "\n" ); document.write( "I have been working on this problem for forever and still am having trouble solving it. Here's what I came up with but I know I'm doing something wrong.\r
\n" ); document.write( "\n" ); document.write( "16!/11!(16-11)! then i write it all out:
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\n" ); document.write( "11! (16-11)!\r
\n" ); document.write( "\n" ); document.write( "16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1
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\n" ); document.write( "11x10x9x8x7x6x5x4x3x2x1x(5x4x3x2x1)
\n" ); document.write( "it gives me some bizarre number. If you could show how to do the work correctly to get an answer that actually makes sense and explain where I went wrong that would be great. Thanks. \n" ); document.write( "
Algebra.Com's Answer #449554 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You need a simpler formula that won't bog you down.\r\n" );
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document.write( "Although \"n%21%2Fr%21%28n-r%29%21\" is a correct formula, and is the one given in most\r\n" );
document.write( "books, it often causes a lot of grief because you often have to write a very\r\n" );
document.write( "long list of factors as you did above, and many of them will cancel out.\r\n" );
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document.write( "A better though equivalent formula that will give the same answer\r\n" );
document.write( "is this:\r\n" );
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document.write( "The number of ways to choose R combinations out of N is:\r\n" );
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document.write( "N(N-1)(N-2)...( )  <-- until there are R factors)\r\n" );
document.write( "覧覧覧覧覧覧覧覧予r\n" );
document.write( "R(R-1)(R-2)...2*1  <-- there will be R factors here for R!\r\n" );
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document.write( "So there will be the same number, R, of factors on the top as on the bottom.\r\n" );
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document.write( "Now we'll even make it easier anytime we are choosing more than half of\r\n" );
document.write( "the number to choose from, as we are in this problem:\r\n" );
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document.write( "Since 11 is more than half of 16, it's easier to look at the problem this\r\n" );
document.write( "way.  Every time we choose 11 players, we choose 5 to NOT PLAY on the team.\r\n" );
document.write( "So choosing 11 to play is the same as choosing the 5 not to play, so it's\r\n" );
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document.write( "\"%2816%2A15%2A14%2A13%2A12%29%2F%285%2A4%2A3%2A2%2A1%29\"\r\n" );
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document.write( "Notice I just started with 16 and came down *15*14, etc. until I had 5 factors\r\n" );
document.write( "on the top and of course there will by 5 factors on the bottom with 5!.  Now\r\n" );
document.write( "you can cancel the 5 into the 15, the 4*3 into the 12 and the 2 into the 14.\r\n" );
document.write( "And you'll end up with 16*3*7*13 or 4368, same as the other tutor got. \r\n" );
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document.write( "Edwin
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