Calculate the number of ability combinations from function usage in Transistor. (answer: 22 billion)

transistor_function_combinations.py

#!/usr/bin/env python3

from math import factorial

def combinations(n):
  ''' Given n functions to be selected, return how many combinations for selecting those functions there are '''
  return int(factorial(16) / factorial(16-n))

def get_all_combinations():
  '''
  - Calculate all possible unique combinations of number of functions in each slot of actives and passives
  - We enforce that no active slot (a,b,c,d) will have more functions than the slot before to eliminate
  having duplicates like (1,2,1,0) and (2,1,1,0)
  '''
  return [(a,b,c,d,p) for a in range(0,3+1) # First active can take any number of functions 0 to 3
                      for b in range(0,a+1) # Second active can take any number of functions 0 to a
                      for c in range(0,b+1) # etc
                      for d in range(0,c+1)
                      for p in range(0,2+1)] # Passives can range from 0 to 2 always

def calculate():
  actives = get_all_combinations()
  print(actives)
  combs = [combinations(sum(act)) for act in actives]
  print('Total combinations: %d from %d slot arrangements' % (sum(combs), len(combs)))

if __name__ == '__main__':
  calculate()