"""
https://en.wikipedia.org/wiki/Combination
"""


def combinations(n: int, k: int) -> int:
 """
 Returns the number of different combinations of k length which can
 be made from n values, where n >= k.

 Examples:
 >>> combinations(10,5)
 252

 >>> combinations(6,3)
 20

 >>> combinations(20,5)
 15504

 >>> combinations(52, 5)
 2598960

 >>> combinations(0, 0)
 1

 >>> combinations(-4, -5)
 ...
 Traceback (most recent call last):
 ValueError: Please enter positive integers for n and k where n >= k
 """

 # If either of the conditions are true, the function is being asked
 # to calculate a factorial of a negative number, which is not possible
 if n < k or k < 0:
 raise ValueError("Please enter positive integers for n and k where n >= k")
 res = 1
 for i in range(k):
 res *= n - i
 res //= i + 1
 return res


if __name__ == "__main__":
 print(
 "The number of five-card hands possible from a standard",
 f"fifty-two card deck is: {combinations(52, 5)}\n",
 )

 print(
 "If a class of 40 students must be arranged into groups of",
 f"4 for group projects, there are {combinations(40, 4)} ways",
 "to arrange them.\n",
 )

 print(
 "If 10 teams are competing in a Formula One race, there",
 f"are {combinations(10, 3)} ways that first, second and",
 "third place can be awarded.",
 )