Algebra.Com's Answer #834771 by ikleyn(52786)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "There are 9 stops on the bus route, the bus carries 13 passengers.
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document.write( "Each of them gets off at  one stop.
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document.write( "(a) What is the probability that no one gets off at at least one stop?
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document.write( "(b) What is the probability that no one gets off at exactly 3 stops?
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document.write( " In this my post, I will solve part (b), ONLY.\r
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document.write( " I re-wrote the condition by substituting the given values
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document.write( " into the text directly, for easy reading and understanding.\r
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document.write( "We can select 3 stops from 9 stops in  =  = 84 ways.\r\n" );
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document.write( "So, for simplicity, we may think now that 3 stops are fixed, where no passengers go out.\r\n" );
document.write( "At other 9-3 = 6 stops some passengers goes out (at least one).\r\n" );
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document.write( "So, the question now is:\r\n" );
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document.write( " | In how many ways 13 passengers can be |\r\n" );
document.write( " | separated/divided in 6 non-empty sets? |\r\n" );
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document.write( " It is the same as to ask: how many solutions does this equation have\r\n" );
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document.write( "  +  +  +  +  +  = 13 (*)\r\n" );
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document.write( " in integer positive numbers?\r\n" );
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document.write( "It is a typical problem to solve using the \"stars and bars\" method.\r\n" );
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document.write( "On Stars and Bars method, see this Wikipedia article \r\n" );
document.write( " https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)\r\n" );
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document.write( "or my lesson on the same subject in this site\r\n" );
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document.write( " Stars and bars method for Combinatorics problems \r\n" );
document.write( " https://www.algebra.com/algebra/homework/Permutations/Stars-and-bars-method-for-Combinatorics-problems-2.lesson\r\n" );
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document.write( "The answer is: this equation (*) has  =  = 792 solutions.\r\n" );
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document.write( "THEREFORE, the answer to question (b) is P =  =  =  = 0.106061.\r\n" );
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document.write( "ANSWER to question (b) is P = = = = 0.106061.\r\n" );
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document.write( "Solved.\r
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