problem 53

"""
There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

In combinatorics, we use the notation, 5C3=10.

In general, nCr=n!r!(n−r)!, where r≤n, n!=n×(n−1)×...×3×2×1, and 0!=1.

It is not until n=23, that a value exceeds one-million: 23C10=1144066.

How many, not necessarily distinct, values of nCr for 1≤n≤100, are greater than one-million?
"""
def factorial(num):
  result = 1
  for i in range(1, num  + 1):
    result *= i
  return result 

counter = 0
for i in range(1, 101):
  for j in range(i + 1):
    solution = factorial(i) / (factorial(j) * factorial(i - j))
    if solution > 1000000:
      counter += 1
print(counter)