#### Binomial Coefficient

N
```def binomial_coefficient(n: int, r: int) -> int:
"""
Find binomial coefficient using Pascal's triangle.

Calculate C(n, r) using Pascal's triangle.

:param n: The total number of items.
:param r: The number of items to choose.
:return: The binomial coefficient C(n, r).

>>> binomial_coefficient(10, 5)
252
>>> binomial_coefficient(10, 0)
1
>>> binomial_coefficient(0, 10)
1
>>> binomial_coefficient(10, 10)
1
>>> binomial_coefficient(5, 2)
10
>>> binomial_coefficient(5, 6)
0
>>> binomial_coefficient(3, 5)
0
>>> binomial_coefficient(-2, 3)
Traceback (most recent call last):
...
ValueError: n and r must be non-negative integers
>>> binomial_coefficient(5, -1)
Traceback (most recent call last):
...
ValueError: n and r must be non-negative integers
>>> binomial_coefficient(10.1, 5)
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
>>> binomial_coefficient(10, 5.1)
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
"""
if n < 0 or r < 0:
raise ValueError("n and r must be non-negative integers")
if 0 in (n, r):
return 1
c = [0 for i in range(r + 1)]
# nc0 = 1
c = 1
for i in range(1, n + 1):
# to compute current row from previous row.
j = min(i, r)
while j > 0:
c[j] += c[j - 1]
j -= 1
return c[r]

if __name__ == "__main__":
from doctest import testmod

testmod()
print(binomial_coefficient(n=10, r=5))
```  