Probability question

Posted 10 years ago
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 I would appreciate help with this question: What is the probability that two nine digit numbers, each using all of the digits 1 through 9, will have exactly two of the digits in the same place in the number?Thank you.-Ron
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Posted 10 years ago
 Oh my. More complex than I had thought.Thank you very much.-Ron
Posted 10 years ago
 We could simulate an experiment with 10^5 random pairs: In[2]:= N[Sum[a = RandomSample[Range[9]]; b = RandomSample[Range[9]];           Boole[Count[a - b, 0] == 2], {10^5}]/10^5]         Out[2]= 0.18364 That's not too far from the exact probability In[3]:= (1/2) Sum[(-1)^j/j!, {j, 0, 7}]Out[3]= 103/560In[4]:= N[%]  Out[4]= 0.183929 See the following link for a proof: The Matching Problem.
Posted 10 years ago
 Not homework, I am having a debate with my adult son and neither of us knows how to answer the question.Thank you.-Ron
Posted 10 years ago
 Is there a Mathematica angle?   This sounds like homework.