Binomial coefficients in Python
Mathematically speaking, the binomial coefficient is rthe number of combinations of items that can be used to form a set nof items, or we can say that this coefficient is the number of ways to choose an outcome in an unordered way from the possibilities.
In this article, we will calculate the binomial coefficient in Python.
scipyCalculate binomial coefficients
in Python using the module
SciPy has two methods for computing binomial coefficients. The first function is called scipy.special.binom(). This function generally handles large values efficiently.
For example,
import scipy.special
print(scipy.special.binom(10, 5))
Output:
252.0
The second function that returns the binomial coefficient is called scipy.special.comb().
For example,
import scipy.special
print(scipy.special.comb(10, 5))
Output:
252.0
math.comb()Calculate binomial coefficient
using function in Python
mathThe function in the module comb()returns a combination of given values that essentially has the same formula as the binomial coefficient. This method is a recent addition to Python 3.8 and later.
For example,
import math
print(math.comb(10, 5))
Output:
252
operatorCalculate binomial coefficients
in Python using the module
In older versions of Python, math.factorialdoes not exist and therefore cannot be used. To compensate for this and generate output in less time, we can use the mathand operatormodules together.
Create a lambda function using operator.mulproduct to get the product of the numbers.
For example,
import math
import operator
from functools import reduce
def product(m, n):
return reduce(operator.mul, range(m, n + 1), 1)
x = 10
y = 5
product(y + 1, x) / product(1, x - y)
Output:
252
math.fact()Calculate binomial coefficient
using function in Python
We can use the function mathin the module fact()to implement the mathematical formula for calculating the binomial coefficient.
Please refer to the code below.
from math import factorial as fact
def binomial(n, r):
return fac(n) // fac(r) // fac(n - r)
print(binomial(10, 5))
Output:
252
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