1. In the wallet, there are six different coins of cents and euros (5 cents, 10 cents, 20 cents, 50 cents, $1 €$ and $2 €$). Three coins are drawn simultaneously and without looking. In how many different ways can the coins be drawn so that their total value is greater than 85 cents?
First solution.

Since the sum of the values of all the coins in cents is $5+10+20+50=85$ cents, we conclude that the sum of the values of any three of these coins will never exceed 85 cents.

To have the sum of the values of the coins exceed 85 cents, at least one of the three coins must be a $1 €$ or $2 €$ coin.

$1 \text{ POINT}$

The coins are drawn simultaneously, so the order in which the drawn coins are recorded does not matter.

The possibilities for the drawn coins with the desired property are:

| $\{1 €, 5$ cents, 10 cents $\}$ | $\{1 €, 5$ cents, 20 cents $\}$ | $\{1 €, 5$ cents, 50 cents $\}$ |
| :--- | :--- | :--- |
| $\{1 €, 10$ cents, 20 cents $\}$ | $\{1 €, 10$ cents, 50 cents $\}$ | $\{1 €, 20$ cents, 50 cents $\}$ |
| $\{2 €, 5$ cents, 10 cents $\}$ | $\{2 €, 5$ cents, 20 cents $\}$ | $\{2 €, 5$ cents, 50 cents $\}$ |
| $\{2 €, 10$ cents, 20 cents $\}$ | $\{2 €, 10$ cents, 50 cents $\}$ | $\{2 €, 20$ cents, 50 cents $\}$ |
| $\{2 €, 1 €, 5$ cents $\}$ | $\{2 €, 1 €, 10$ cents $\}$ |  |
| $\{2 €, 1 €, 20$ cents $\}$ | $\{2 €, 1 €, 50$ cents $\}$ |  |

8 POINTS

(Note: 1 POINT is awarded for every two correctly written possibilities. The number of points awarded must be an integer.)

Such coins can be drawn in 16 different ways.

1 POINT TOTAL 10 POINTS

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