Python – math.comb() method

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 module
import math

n = 10
k = 2

# Get the number of ways to choose
# k items from n items without
# repetition and without order
nCk = math.comb(n, k)
print(nCk)

n = 5
k = 3

# Get the number of ways to choose
# k items from n items without
# repetition and without order
nCk = math.comb(n, k)
print(nCk)

Output:

45
10

Code #2: When k > n

# Python Program to explain math.comb() method

# Importing math module
import math

# When k > n
# math.comb(n, k) returns 0.
n = 3
k = 5

# Get the number of ways to choose
# k items from n items without
# repetition and without order
nCk = 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 module
import math

n = 5
k = 2

# Find the coefficient of k-th
# term in the expansion of
# expression (1 + x)^n
nCk = math.comb(n, k)
print(nCk)

n = 8
k = 3

# Find the coefficient of k-th
# term in the expansion of
# expression (1 + x)^n
nCk = math.comb(n, k)
print(nCk)

Output:

10
56

Reference: Python math library