Choice of sum

A list contains the integers $1 \dots n$. How many ways can you choose $k$ numbers from the list so that their sum is $x$?

You may assume that $1 \le n \le 10$ and that $1 \le k \le n$. The algorithm should be efficient in all these cases.

In a file getsum.py, implement a function count that returns the desired count.

def count(n, k, x):
    # TODO

if __name__ == "__main__":
    print(count(1, 1, 1)) # 1
    print(count(5, 2, 6)) # 2
    print(count(8, 3, 12)) # 6
    print(count(10, 4, 20)) # 16

Explanation: When $n=8$, $k=3$ and $x=12$, the answer is $6$. Here the list is $[1,2,3,4,5,6,7,8]$ and the possible ways are $[1,3,8]$, $[1,4,7]$, $[1,5,6]$, $[2,3,7]$, $[2,4,6]$ and $[3,4,5]$.