In [1]:

    

import math


    

In [2]:

    

print(math.factorial(5))


    

    




120

In [3]:

    

print(math.factorial(0))


    

    




1

In [5]:

    

# print(math.factorial(1.5))
# ValueError: factorial() only accepts integral values


    

In [4]:

    

# print(math.factorial(-1))
# ValueError: factorial() not defined for negative values


    

In [6]:

    

def permutations_count(n, r):
    return math.factorial(n) // math.factorial(n - r)


    

In [8]:

    

print(permutations_count(4, 2))


    

    




12

In [7]:

    

print(permutations_count(4, 4))


    

    




24

In [9]:

    

def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))


    

In [10]:

    

print(combinations_count(4, 2))


    

    




6

In [11]:

    

def combinations_with_replacement_count(n, r):
    return combinations_count(n + r - 1, r)


    

In [12]:

    

print(combinations_with_replacement_count(4, 2))


    

    




10