5. In how many ways can we pay an amount of 20 kuna using coins of $5 \mathrm{kn}$, $2 \mathrm{kn}$, and $1 \mathrm{kn}$, so that each type of coin is used at least once?

## Tasks worth 10 points:
First method:

When each coin is used once, we paid 8 kn.

1 POINT

There is still 12 kuna to be paid, using any coins.

1 POINT

All payment options can be represented in a table:

| $\mathbf{5 k n}$ | 2 | 2 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| $\mathbf{2} \mathbf{k n}$ | 1 | 0 | 3 | 2 | 1 | 0 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| $\mathbf{1} \mathbf{k n}$ | 0 | 2 | 1 | 3 | 5 | 7 | 0 | 2 | 4 | 6 | 8 | 10 | 12 |

The required amount can be paid in 13 ways.