# Python – math.comb() method

• Last Updated : 23 Jan, 2020

Math module in Python contains a number of mathematical operations, which can be performed with ease using the module. math.comb() method in Python is used to get the number of ways to choose k items from n items without repetition and without order. It basically evaluates to n! / (k! * (n – k)!) when k n. It is also known as binomial coefficient because it is equivalent to the coefficient of k-th term in polynomial expansion of the expression (1 + x)n.
This method is new in Python version 3.8.

Syntax: math.comb(n, k)

Parameters:
n: A non-negative integer
k: A non-negative integer

Returns: an integer value which represents the number of ways to choose k items from n items without repetition and without order.

Code #1: Use of math.comb() method

 # Python Program to explain math.comb() method  # Importing math moduleimport math  n = 10k = 2  # Get the number of ways to choose# k items from n items without# repetition and without ordernCk = math.comb(n, k)print(nCk)  n = 5k = 3  # Get the number of ways to choose# k items from n items without# repetition and without ordernCk = math.comb(n, k)print(nCk)

Output:

45
10

Code #2: When k > n

 # Python Program to explain math.comb() method  # Importing math moduleimport math  # When k > n # math.comb(n, k) returns 0.n = 3k = 5  # Get the number of ways to choose# k items from n items without# repetition and without ordernCk = math.comb(n, k)print(nCk)

Output:

0

Code #3: Use of math.comb() method to find coefficient of k-th term in binomial expansion of expression (1 + x)n

 # Python Program to explain math.comb() method  # Importing math moduleimport math  n = 5k = 2  # Find the coefficient of k-th# term in the expansion of # expression (1 + x)^nnCk = math.comb(n, k)print(nCk)  n = 8k = 3  # Find the coefficient of k-th# term in the expansion of # expression (1 + x)^nnCk = math.comb(n, k)print(nCk)

Output:

10
56

Reference: Python math library

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