Problem Statement
Definition
- Class:
- TwoLotteryGames
- Method:
- getHigherChanceGame
- Parameters:
- int, int, int
- Returns:
- double
- Method signature:
- double getHigherChanceGame(int n, int m, int k)
- (be sure your method is public)
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
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.
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.
8
2
1
Returns: 0.4642857142857143
8
4
2
Returns: 0.7571428571428571
8
3
1
Returns: 0.8214285714285714
2
1
1
Returns: 0.5
2
1
1
Returns: 0.5
3
1
1
Returns: 0.3333333333333333
3
2
1
Returns: 1.0
3
2
2
Returns: 0.3333333333333333
4
1
1
Returns: 0.25
4
2
1
Returns: 0.8333333333333334
4
2
2
Returns: 0.16666666666666666
4
3
1
Returns: 1.0
4
3
2
Returns: 1.0
4
3
3
Returns: 0.25
5
1
1
Returns: 0.2
5
2
1
Returns: 0.7
5
2
2
Returns: 0.1
5
3
1
Returns: 1.0
5
3
2
Returns: 0.7
5
3
3
Returns: 0.1
5
4
1
Returns: 1.0
5
4
2
Returns: 1.0
5
4
3
Returns: 1.0
5
4
4
Returns: 0.2
6
1
1
Returns: 0.16666666666666666
6
2
1
Returns: 0.6
6
2
2
Returns: 0.06666666666666667
6
3
1
Returns: 0.95
6
3
2
Returns: 0.5
6
3
3
Returns: 0.05
6
4
1
Returns: 1.0
6
4
2
Returns: 1.0
6
4
3
Returns: 0.6
6
4
4
Returns: 0.06666666666666667
6
5
1
Returns: 1.0
6
5
2
Returns: 1.0
6
5
3
Returns: 1.0
6
5
4
Returns: 1.0
6
5
5
Returns: 0.16666666666666666
7
1
1
Returns: 0.14285714285714285
7
2
1
Returns: 0.5238095238095238
7
2
2
Returns: 0.047619047619047616
7
3
1
Returns: 0.8857142857142857
7
3
2
Returns: 0.37142857142857144
7
3
3
Returns: 0.02857142857142857
7
4
1
Returns: 1.0
7
4
2
Returns: 0.8857142857142857
7
4
3
Returns: 0.37142857142857144
7
4
4
Returns: 0.02857142857142857
7
5
1
Returns: 1.0
7
5
2
Returns: 1.0
7
5
3
Returns: 1.0
7
5
4
Returns: 0.5238095238095238
7
5
5
Returns: 0.047619047619047616
7
6
1
Returns: 1.0
7
6
2
Returns: 1.0
7
6
3
Returns: 1.0
7
6
4
Returns: 1.0
7
6
5
Returns: 1.0
7
6
6
Returns: 0.14285714285714285
8
1
1
Returns: 0.125
8
2
1
Returns: 0.4642857142857143
8
2
2
Returns: 0.03571428571428571
8
3
1
Returns: 0.8214285714285714
8
3
2
Returns: 0.2857142857142857
8
3
3
Returns: 0.017857142857142856
8
4
1
Returns: 0.9857142857142858
8
4
2
Returns: 0.7571428571428571
8
4
3
Returns: 0.24285714285714285
8
4
4
Returns: 0.014285714285714285
8
5
1
Returns: 1.0
8
5
2
Returns: 1.0
8
5
3
Returns: 0.8214285714285714
8
5
4
Returns: 0.2857142857142857
8
5
5
Returns: 0.017857142857142856
8
6
1
Returns: 1.0
8
6
2
Returns: 1.0
8
6
3
Returns: 1.0
8
6
4
Returns: 1.0
8
6
5
Returns: 0.4642857142857143
8
6
6
Returns: 0.03571428571428571
8
7
1
Returns: 1.0
8
7
2
Returns: 1.0
8
7
3
Returns: 1.0
8
7
4
Returns: 1.0
8
7
5
Returns: 1.0
8
7
6
Returns: 1.0
8
7
7
Returns: 0.125