permcomb.txt

## Meaning

- Permutation comes from Latin "permutare", meaning to change thoroughly ("per" = thoroughly, "mutare" = to change).
→ So permutations are about changing the order — the different arrangements matter.

- Combination comes from Latin "combinare", meaning to join together ("com" = together, "bini" = two by two).
→ So combinations are about joining together, not worrying about the order — just grouping.

## Summary by meaning

Permutation → changing order (order matters)

Combination → joining together (order doesn't matter)

## Simple example:

Suppose we have **3 people** — **Alice (A)**, **Bob (B)**, and **Charlie (C)**.

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### Combinations (Order **Doesn't** Matter)

You are **picking 2 people** to form a committee.

Possible groups:
- A and B
- A and C
- B and C

> (Picking A then B is **the same** as picking B then A.)

**Total combinations**: 3 groups

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### Permutations (Order **Matters**)

You are **picking a president and a vice president**.

Possible ordered pairs:
- A then B
- A then C
- B then A
- B then C
- C then A
- C then B

> (A then B is **different** from B then A.)

**Total permutations**: 6 arrangements

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### Quick Visual Table

| Picking 2 people | **Combination**        | **Permutation** |
|:-----------------|:------------------------|:----------------|
| A and B           | Same                    | A then B        |
| B and A           | Same as A and B          | B then A        |
| A and C           | Same                    | A then C        |
| C and A           | Same as A and C          | C then A        |
| B and C           | Same                    | B then C        |
| C and B           | Same as B and C          | C then B        |

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### Key Difference

- **Combinations** → Group matters, **order doesn't**  
- **Permutations** → **Order matters**