Algebra.Com's Answer #846489 by ikleyn(52855)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Good afternoon,
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document.write( "Please help me?
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document.write( "If there are 12 horses in a race what are the odds of selecting the exact finishing order of all 12 horses?
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document.write( "Could you please give me a formula to calculate any other odds also?
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document.write( "As in, 10 horses, 7 horses or other numbers of horses.
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document.write( "Thank you in anticipation.
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document.write( "Regards
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document.write( "Faye
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document.write( "(a) 12 horses. Want to find the probability of guessing right order for all 12 horses.\r\n" );
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document.write( " In all, there are 12! = 12*11*10* . . . * 3*2*1 = 479001600 different finishing orders.\r\n" );
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document.write( " Of them, only one order is winning.\r\n" );
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document.write( " Therefore, the probability to guess the winning order is P =  =  = 2.08768E-09,\r\n" );
document.write( " which is very small number.\r\n" );
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document.write( " In terms of odds, the odds to guess the winning order correctly are 1 against 479001600-1 = 47900159.\r\n" );
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document.write( "(b) 12 horses. Want to find the probability of guessing right order for some particular 10 horses.\r\n" );
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document.write( " Again, there are 12! = 12*11*10* . . . * 3*2*1 = 479001600 different finishing orders.\r\n" );
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document.write( " Winning orders are those, where these particular 10 horses finish in the assigned order,\r\n" );
document.write( " while 12-10 = 2 horses can finish in any arbitrary order among remaining positions.\r\n" );
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document.write( " So, the number of winning orders is 2! = 2 (two last horses finish in any order among remaining positions).\r\n" );
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document.write( " Therefore, the probability to guess the winning order is P =  =  = 4.17535E-09,\r\n" );
document.write( " which is also very small number.\r\n" );
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document.write( " In terms of odds, the odds to guess the winning order correctly are 2 against 479001600-2 = 47900158.\r\n" );
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document.write( "(c) 12 horses. Want to find the probability of guessing right order for some particular 7 horses.\r\n" );
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document.write( " Again, there are 12! = 12*11*10* . . . * 3*2*1 = 479001600 different finishing orders.\r\n" );
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document.write( " Winning orders are those, where these particular 7 horses finish in the assigned order,\r\n" );
document.write( " while 12-7 = 5 horses can finish in any arbitrary order among remaining positions.\r\n" );
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document.write( " So, the number of winning orders is 5! = 5*4*3*2*1 = 120 (5 last horses finish in any order among remaining positions).\r\n" );
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document.write( " Therefore, the probability to guess the winning order is P =  =  = 2.50521E-07,\r\n" );
document.write( " which is still very small number.\r\n" );
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document.write( " In terms of odds, the odds to guess the winning order correctly are 120 against 479001600-120 = 479001480.\r\n" );
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document.write( "Thus you have now standard templates on how to make reasoning and
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document.write( "how to calculate the probabilities and the odds in any other appropriate case.\r
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