**Permutation **– position (order) matters. = N! / (N – r)!.

**Building words**with {a,b,c} are also permutation problem with r = {1,2,3..N}

**Combination** – position (order) doesn’t matter = N! / (N – r)! * r! . Combination is a part of Permutation set. **All possible combination** means, generating combination for r = {0,1.. N}. For set {1,2,3}, the **powerset** is

_{r = 0, combinations {}}_{r = 1, combinations {1},{2},{3}}_{r = 2, combinations {1,2},{2,3},{3,1}}_{r = 3, combinations {1,2,3}}

**Coins problems**are combination problems with r= {1,2,3..N}. ex.**combination of coins sum up to an amount**. Repetition of coin is allowed.

- Ex. Amount =4 with coins{1,2,3}, combinations are {1,1,1,1},{1,1,2},{2,2},{1,3}
**.**Take all possible combinations of coins - {1},{2},{3}
- {1,1},{1,2},{
**1,3**},{**2,2**},{2,3},{3,3} - {1,1,1},{2,2,2},{3,3,3},{
**1,1,2**},{1,1,3},{1,2,3},{1,2,2},{1,3,3},{2,3,3} - {
**1,1,1,1**},{2,2,2,2},{3,3,3,3}

Спасибо, давно искал

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