Сочетания и перестановки

import math

# Combinations C(n, r): order doesn't matter
n, r = 10, 3
c = math.comb(n, r)
print(f"C({n},{r}) = {c}")  # 120

# Permutations P(n, r): order matters
p = math.perm(n, r)
print(f"P({n},{r}) = {p}")  # 720

# Manual calculation
def combinations(n, r):
    return math.factorial(n) // (math.factorial(r) * math.factorial(n - r))

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

# All actual combinations
from itertools import combinations as combs, permutations as perms

items = ["A", "B", "C", "D"]
for combo in combs(items, 2):
    print(combo)  # ('A','B'), ('A','C'), ...

for perm in perms(items, 2):
    print(perm)   # ('A','B'), ('A','C'), ('B','A'), ...

# Combinations with repetition
from itertools import combinations_with_replacement
for c in combinations_with_replacement("ABC", 2):
    print(c)  # ('A','A'), ('A','B'), ...