document.write( "Question 971427: 15 gymnasts are competing in a national competition and will be ranked from 1 to 5
\n" ); document.write( "top five gymnasts will then move on to the world competition how many different
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Algebra.Com's Answer #594056 by Edwin McCravy(20056)\"\" \"About 
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15 gymnasts are competing in a national competition and will be ranked from 1 to 5
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document.write( "Order matters in this problem because of the rankings #1 through #5.\r\n" );
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document.write( "There are 15 ways to choose gymnast #1.\r\n" );
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document.write( "For each of those 15 ways to choose gymnast #1, there remain 14 ways\r\n" );
document.write( "to choose gymnast #2.\r\n" );
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document.write( "That's 15*14 ways to choose gymnasts #1 and #2.\r\n" );
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document.write( "For each of those 15*14 ways to choose gymnasts #1 and #2, there remain\r\n" );
document.write( "13 ways to choose gymnast #3.\r\n" );
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document.write( "That's 15*14*13 ways to choose gymnasts #1,#2, and #3.\r\n" );
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document.write( "For each of those 15*14*13 ways to choose gymnasts #1,#2, and #3, there \r\n" );
document.write( "remain 12 ways to choose gymnast #4.\r\n" );
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document.write( "That's 15*14*13*12 ways to choose gymnasts #1,#2,#3 and #4.\r\n" );
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document.write( "For each of those 15*14*13*12 ways to choose gymnasts #1,#2,#3 and #4,\r\n" );
document.write( "there remain 11 ways to choose gymnast #5.\r\n" );
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document.write( "That's 15*14*13*12*11 ways to choose gymnasts #1,#2,#3,#4 and #5.\r\n" );
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document.write( "So the answer is 15*14*13*12*11 = 360360.\r\n" );
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document.write( "That is sometimes called \"15 Position 5\" or \"15P5\" or \"P(15,5)\" or \r\n" );
document.write( "\"The number of permutations of 15 things taken 5 at a time. \r\n" );
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document.write( "The general formula for the number of n things taken r at a time\r\n" );
document.write( "is \"nPr+=+n%21%2F%28n-r%29%21\".\r\n" );
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document.write( "So \r\n" );
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document.write( "Edwin
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