import math
def choose(n: int, k: int) -> int:
return math.comb(n, k)
def poker_hands() -> int:
# 52 choose 5.
return math.comb(52, 5)
def out_of_range(n: int, k: int) -> int:
# k > n -> 0 (with non-negative args; negative args raise in Python).
return math.comb(n, k)
def symmetric(n: int) -> int:
# comb(n, 0) + comb(n, n) == 2 (exercises the min(k, n-k) path).
return math.comb(n, 0) + math.comb(n, n)