Python math.comb() - Number of Combinations

Python math.comb()

math.comb(n, k) function returns the number of ways to select k items from n items without repeating the items and without order.

comb(n, k) = n! / ( k! * (n - k)! )

comb() function is available since Python version 3.8.

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Syntax

The syntax to call comb() function is

math.comb(n, k)

where

Parameter	Required	Description
n	Yes	An integer value.
k	Yes	An integer value.

If n or k is not integer, then comb() raises TypeError.

If n or k is negative, then comb() raises ValueError.

If n is less than k, then comb() returns 0.

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Examples

Number of combinations for selection 4 out of 9 items, without repetition and without considering order.

Python Program

import math

n = 9
k = 4
result = math.comb(n, k)
print('comb(n, k) :', result)

Output

comb(n, k) : 126

Number of combinations when n is negative.

Python Program

import math

n = -9
k = 4
result = math.comb(n, k)
print('comb(n, k) :', result)

Output

ValueError: n must be a non-negative integer

Number of combinations when n is not integer.

Python Program

import math

n = 9.2
k = 4
result = math.comb(n, k)
print('comb(n, k) :', result)

Output

TypeError: 'float' object cannot be interpreted as an integer

Number of combinations when n is less than k.

Python Program

import math

n = 2
k = 4
result = math.comb(n, k)
print('comb(n, k) :', result)

Output

comb(n, k) : 0

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Summary

In this Python Examples tutorial, we learned the syntax of, and examples for math.comb() function.