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
Class:TwoLotteryGames
Method:getHigherChanceGame
Parameters:int, int, int
Returns:double
Method signature:double getHigherChanceGame(int n, int m, int k)


NOTES
-Your return must have relative or absolute error less than 1E-9.


CONSTRAINTS
-n will be between 2 and 8, inclusive.
-m will be between 1 and n-1, inclusive.
-k will be between 1 and m, inclusive.


EXAMPLES

0)
3
2
1

Returns: 1.0

Here you and the organizers will choose 2 numbers among 3. It will be 4 numbers in total, so at 
least 1 number in your and their sets will repeat for sure.

1)
3
1
1

Returns: 0.3333333333333333

Now you and the organizers will choose 1 number. These numbers will be the same with probability 
1/3.

2)
8
2
1

Returns: 0.4642857142857143



3)
8
4
2

Returns: 0.7571428571428571



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