Course

A course consists of $8$ weeks, each of which has $8$ tasks. You pass the course, if you complete at least $5$ tasks each week.

How many ways can you pass the course so that you complete a total of $x$ tasks? Two ways of passing the course are considered different, if the lists of completed tasks in the order of completion are different.

You may assume that $1 \le x \le 100$. The algorithm should be efficient in all these cases. The code must compute the results and not just return precomputed results.

In a file course.py, implement a function count that returns the number of ways to complete the course.

def count(x):
    # TODO

if __name__ == "__main__":
    print(count(40)) # 78913132667888442497725132524762783866832203758436352000000000
    print(count(55)) # 320424698352073967965876852452014215914220727801318938295395908593909760000000000000
    print(count(64)) # 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000
    print(count(100)) # 0

Explanation: When $x=40$, exactly $5$ tasks must be completed each week. The tasks can be completed in $40!$ different orders and the tasks for each week can be chosen in ${8 \choose 5}$ ways. Thus answer is $40! \cdot {8 \choose 5}^8$. When $x=64$, all tasks are completed and thus the answer is $64!$.