Partial Permutations

We are back with the permutations once again. This time we are set the task to find the number of partial permutations that can be formed from a set of numbers. We are given two integers, n and k, where the range of 1 to n is the set of numbers and k is the length of the partial mutations and should return the number of partial mutations modulo 1 000 000.

Sample data:
21 7

Expected output:
51200

I wrote two programs that solve this problem. The first uses the math module permutations to find all possible permutations and count them. You can have a look at the code below. However, this program is inefficient which is why I chose to write a second, faster program.

Slow approach:

import itertools
n = 21
k = 7
count = 0
for p in itertools.permutations(range(1, n + 1), k):
    count += 1
print(count % 1000000)

Faster approach:

n = 21
k = 7

partial_perm = 1

for i in range(k):
    partial_perm *= (n - i)
print(partial_perm % 1000000)

Both of the programs work and complete the problem within the time limits of Rosalind, but the second program is much faster than the first one.