Python Combinatorics Basics: Permutations and Combinations

Count different selections and arrangements by asking whether order matters.

What You Will Learn

Combinations choose a group without caring about order, while permutations count ordered arrangements. Factorial counts arrangements of all distinct items. For example, choosing two teammates differs from assigning first and second place. Functions such as math.comb and math.perm return exact integers.

For floating-point results, remember that stored values are approximations. Rounding a displayed value does not change the exact value used by later calculations.

Step-by-Step Example

The example below makes the behavior visible with small input values that you can change safely.

import math

participants = 5
print(math.comb(participants, 2))
print(math.perm(participants, 2))
print(math.factorial(4))

How the Example Works

The imports provide the standard-library tools used in the demonstration: math.
The variable participants holds the result of 5. Later lines use that value or inspect how it changes.
The print() calls make the return values or state visible so you can compare them with the explanation and check your prediction.

Expected output from the example:

10
20
24

When You Would Use This

This operation can support measurements, numeric reports, simulations, or input validation. Choose integer operations when exact integer answers are required, and check floating-point rounding when displaying measured values. Validate units and input domains before using the result in a calculation.

Practice: Modify the Code

Count two-person teams from six players and ordered first/second finishes.

Verify the changed output against the behavior described above, including the relevant invalid or boundary case.

For complete parameters and version details, consult the official Python documentation.

Common Beginner Mistakes

Using permutations when only the chosen group matters.
Forgetting that a combination cannot select more distinct positions than exist.

Key Takeaways

Count different selections and arrangements by asking whether order matters.
Combinations choose a group without caring about order, while permutations count ordered arrangements.
Apply this operation only after checking the assumptions and input conditions shown in the example.