**Falling factorial** is a notion used in counting issues to describe the product of decreasing integers up to a given point. It is especially helpful when selecting a certain number of elements from a bigger collection is required, and order is important.

The sum of the first

The falling factorial, which we can use to select the top

The recurrence connection can be used to relate the falling factorial to the factorial:

By using this relation, we may create a recursive definition of the falling factorial by expressing it in terms of a smaller falling factorial.

Let’s implement the falling factorial in Python:

import mathdef falling_factorial(n, k):if n < k:raise ValueError("n must be greater than or equal to k")result = math.factorial(n) // math.factorial(n - k)return result# Example usagen = 10k = 3result = falling_factorial(n, k)print(f"The falling factorial ({n})_{k} is: {result}")

**Line 1:**Here, we import the`math`

module.**Lines 3–9:**We calculate the falling factorial of a given number`n`

with`k`

terms.**Lines 5–6:**We check if the value of`n`

(representing the base) is less than the value of`k`

(representing the number of terms). If`n`

is less than`k`

, it means there aren't enough terms to calculate the falling factorial, so it raises a`ValueError`

with an appropriate message.**Line 8:**We calculate the falling factorial using the formula`n! / (n - k)!`

. It first calculates the factorial of`n`

using`math.factorial(n)`

and then divides it by the factorial of`n - k`

to get the falling factorial. The`//`

operator is used for integer division to ensure the result is an integer.**Line 9:**It returns the calculated falling factorial value.

**Lines 12–15:**We print the result is an example of using the function with`n=10`

and`k=3`

.

Copyright ©2024 Educative, Inc. All rights reserved

TRENDING TOPICS