A factorial is the product of all positive integers from a natural number down to one. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120 and 3! = 6. section 2.2.3
Factorials count ordered selections without replacement: n! / (n − r)! accounts for the progressively smaller number of available choices. With five runners and three positions, the result is 60 possible rankings. section 2.2.3
Computing a permutation count in Python
Use math.factorial(n) / math.factorial(n − r) to calculate the number of ordered selections without replacement; for n = 5 and r = 3, Python returns 60. section 2.2.3
>>> import math
>>> permutations = math.factorial(n) / math.factorial(n - r)
>>> print(f'Number of permutations without replacement: '
>>> f'{permutations}')
Number of permutations without replacement: 60
Python listing for calculating permutations without replacement with factorials. section 2.2.3
