🧮 Formula
- nPr = n! / (n – r)!
- nCr = n! / [r! × (n – r)!]
📘 Description
Permutations and Combinations are fundamental concepts in mathematics, particularly in the field of combinatorics. They are used to count the number of ways to select or arrange items.
- Permutation (nPr): Counts the number of ways to arrange r items out of n (order matters).
- Combination (nCr): Counts the number of ways to choose r items out of n (order doesn’t matter).
🔍 Example
Question: How many ways can you choose 3 students out of 5 to assign to different tasks (permutation)? And how many ways to choose 3 students to join a team (combination)?
n = 5, r = 3
- nPr = 5! / (5-3)! = 120 / 2 = 60
- nCr = 5! / (3! × 2!) = 120 / (6 × 2) = 10
🌍 Real-World Use Cases
- Permutations: Arranging books on a shelf, creating passwords, assigning roles in a team.
- Combinations: Selecting lottery numbers, choosing a committee, forming a project team.