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Python 3.11.3 (main, Apr  7 2023, 00:39:07) [Clang 14.0.7 (https://android.googlesource.com/toolchain/llvm-project 4c603efb0 on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import itertools
>>> a = set(range(1, 526))
>>> len(list(itertools.combinations(a, 35)))

import itertools
a = set(range(1, 526))
n = itertools.combinations(a, 35) # returns a generator, not a list
count = 0
try:
    while True:
        element = next(n)
        count += 1
        # Process the element
except StopIteration:
    pass
print(count)

n! / (k! * (n-k)!) => 525! / (35! * (525-35)!) => 525! / (35! * 490!)

def factorial_loop(n):
    factorial = 1
    for i in range(1, n + 1):
        factorial *= i
    return factorial

from decimal import Decimal, getcontext

getcontext().prec = 500

n = int(input("Enter a number n: "))
k = int(input("Enter a number k: "))

numerator = Decimal(factorial_loop(n))
denominator = Decimal(factorial_loop(k) * factorial_loop(n-k))

result = numerator / denominator

print("numerator: ", numerator)
print("denominator: ", denominator)
print("result: ", result)

4875197867478707228958513876216391120239539892113911200

BigInteger dividend = 1;
for (int i = 491; i <= 525; i++)
{
    dividend *= i;
}
BigInteger divisor = 1;
for (int i = 2; i <= 35; i++)
{
    divisor *= i;
}
BigInteger result = dividend / divisor;

Python 3.11.3 (main, Apr  7 2023, 00:39:07) [Clang 14.0.7 (https://android.googlesource.com/toolchain/llvm-project 4c603efb0 on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import math
>>> f, n, k = math.factorial, 525, 35
>>> f(n) // (f(k) * f(n-k))
4875197867478707228958513876216391120239539892113911200
>>>

>>> import math; from time import perf_counter as pk; start,f,n,k = pk(), math.factorial,525,450; f(n) // (f(k) * f(n-k)); perf_counter() - start
160238594860256432756426324474230582470146598379168712962500960567057295818091919639830840080
0.0005006769933970645