
from math import factorial


def 						UpperCAmelCase			(	a_		,   a_						)		->	int:







				"""simple docstring"""



				if n < k or k < 0:
								raise ValueError("Please enter positive integers for n and k where n >= k"						)
				return factorial(a_						) // (factorial(a_						) * factorial(n - k						))


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.',
					)






from math import sqrt

def 					UpperCAmelCase_							(      __UpperCAmelCase						:	int							)					-> bool:

      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5			,			int(sqrt(__UpperCAmelCase							) + 1							)			,			6							):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True

def 					UpperCAmelCase_							(      __UpperCAmelCase						:	int = 1_00_01							)					-> int:
      SCREAMING_SNAKE_CASE_							=			0
      SCREAMING_SNAKE_CASE_							=			1
      while count != nth and number < 3:
            number += 1
            if is_prime(__UpperCAmelCase							):
                  count += 1
      while count != nth:
            number += 2
            if is_prime(__UpperCAmelCase							):
                  count += 1
      return number


if __name__ == "__main__":
   print(f'''{solution() = }''')