


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 __future__ import annotations





def __UpperCAmelCase       (		__A ,						__A ,						__A ,						)						->					tuple:



       '''simple docstring'''





       if (electron_conc, hole_conc, intrinsic_conc).count(0			) != 1:
              raise ValueError("You cannot supply more or less than 2 values"			)
       elif electron_conc < 0:
              raise ValueError("Electron concentration cannot be negative in a semiconductor"			)
       elif hole_conc < 0:
              raise ValueError("Hole concentration cannot be negative in a semiconductor"			)
       elif intrinsic_conc < 0:
              raise ValueError(
                  "Intrinsic concentration cannot be negative in a semiconductor"			)
       elif electron_conc == 0:
              return (
                  "electron_conc",
                  intrinsic_conc**2 / hole_conc,
              )
       elif hole_conc == 0:
              return (
                  "hole_conc",
                  intrinsic_conc**2 / electron_conc,
              )
       elif intrinsic_conc == 0:
              return (
                  "intrinsic_conc",
                  (electron_conc * hole_conc) ** 0.5,
              )
       else:
              return (-1, -1)


if __name__ == "__main__":
    import doctest

    doctest.testmod()





