Difference in output of sympy.binomial vs scipy.special.comb

Question

Why does the following code that calls comb produce the wrong output?

from scipy.special import comb
from sympy import binomial


def coup(n=100, m=10):
    expectation = 0
    for j in range(1, n + 1):
        coeff = ((-1)**(j-1)) * comb(n, j)
        denominator = 1 - (comb(n - j, m) / comb(n, m))
        expectation += coeff / denominator
    
   print(expectation)

   # output: 1764921496446.9807
   # correct output when using binomial: 49.9445660566641

The code does not call comb. Also you should use brackets for (-1)**(j-1). — Oscar Benjamin
– Oscar Benjamin, Commented Feb 27 at 11:51

Karan Shishoo · Accepted Answer · 2025-02-27 07:23:05Z

4

You need to include the exact parameter as True for the comb function if you want it to have full precision and not just floating point precision. (It defaults to False) for example -

comb(100,15) - binomial(100,15)

would give an output of -32, but

comb(100,15, exact=True) - binomial(100,15)

gives an output of 0

This is as per SciPy docs - https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.comb.html

answered Feb 27 at 7:23

Karan Shishoo

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