https://file.aiquickdraw.com/mathbot/file/1725482314881amohj5os.jpg

The image contains two mathematical problems. Let me analyze and solve them for you:

### Problem 1: Solve using the given formula
The formula provided in the image is:
\[
P(n, r) = \frac{n!}{(n-r)!}
\]
where \( P(n, r) \) represents the number of permutations of \( n \) items taken \( r \) at a time.

The problem asks to find the number of ways to arrange:
- **5 distinct shapes (points, circles, lines, and squares).**

Let’s assume you need to find the number of permutations of these 5 shapes taken all 5 at a time.

### Solution:
\[
P(5, 5) = \frac{5!}{(5-5)!} = \frac{5!}{0!} = \frac{120}{1} = 120
\]

So, there are 120 different ways to arrange the 5 shapes.

### Problem 2: Combinations of Coins
The second question is:
- **If you grab three coins from a jar of change, how many different combinations of coins are possible?**

This is a classic combinations problem since the order of selecting the coins does not matter.

### Solution:
If we assume there are \( n \) different types of coins in the jar and you are choosing 3, then the number of combinations is calculated by:
\[
C(n, 3) = \frac{n!}{3!(n-3)!}
\]

However, the problem doesn't specify the number of distinct coin types or the total number of coins. Assuming the jar contains an infinite supply of each coin type (let’s say pennies, nickels, dimes, and quarters), the number of combinations is more complex and depends on the distribution of these coin types.

Do you need more details on the second problem? Also, would you like a more detailed breakdown of these solutions?

Solve the following problems using the given formula and combinations:

1. The jar of change contains:
   - points,
   - circles,
   - lines, and
   - squares.

2. If you grab three coins from a jar of change, how many different combinations of coins are possible?

Explore how to calculate permutations of different shapes and determine the number of combinations of coins using fundamental mathematical formulas. This problem is suitable for high school students and involves permutations and combinations concepts.

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