import math
def arrange(n: int, k: int) -> int:
return math.perm(n, k)
def license_plates() -> int:
# 10 distinct digits taken 3 at a time, order matters: 10*9*8.
return math.perm(10, 3)
def all_of(n: int) -> int:
# One-arg form: perm(n) == n! (lowers to factorial).
return math.perm(n)
def out_of_range(n: int, k: int) -> int:
# k > n -> 0 (with non-negative args; negative args raise in Python).
return math.perm(n, k)
def empty_pick(n: int) -> int:
# perm(n, 0) == 1 (empty product).
return math.perm(n, 0)