What is the difference between permutations and combinations?

Mathematics

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Answer

n!/(n−r)!

Both count ways to select items from a group, but they differ in whether order matters.

Permutations (order matters): P(n,r) = n!/(n−r)! Example: How many ways can 3 people finish a race from 10 runners? P(10,3) = 10×9×8 = 720

Combinations (order doesn't matter): C(n,r) = n!/[r!(n−r)!] Example: How many ways to choose 3 people for a committee from 10? C(10,3) = 120

Quick rule: If rearranging the selection gives a different outcome → permutation. If not → combination.

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Both count ways to select items from a group, but they differ in whether order matters.

What is the difference between permutations and combinations?
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Both count ways to select items from a group, but they differ in whether order matters. Permutations (order matters): P(n,r) = n!/(n−r)! Example: How many ways can 3 people finish a race from 10 runners? P(10,3) = 10×9×8 = 720 Combinations (order doesn't matter): C(n,r) = n!/[r!(n−r)!] Example: How many ways to choose 3 people for a committee from 10? C(10,3) = 120 Quick rule: If rearranging the selection gives a different outcome → permutation. If not → combination.