Problem Statement  
Yesterday, when you were passing by the newsstand near your home, you saw an advertisement for lottery games. The advertisement said "Choose m different numbers between 1 and n, inclusive. We will also randomly pick m different numbers between 1 and n, inclusive, and if you have at least k numbers in common with us, you win!". You want to know the probability of winning this lottery game. You are given three integers n, m, and k as described above. Return the probability of winning the game.  
Definition  
 
Notes  
  Your return must have relative or absolute error less than 1E9.  
Constraints  
  n will be between 2 and 8, inclusive.  
  m will be between 1 and n1, inclusive.  
  k will be between 1 and m, inclusive.  
Examples  
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