An ice cream store offers 28 flavors of ice cream.  One of their specials is a bowl that contains four scoops of ice cream.  How many such bowls are possible if you can have the same type of ice cream for more than one scoop?

In this problem, we're dealing with combinations where repetition is allowed. Since there are 28 flavors, and you can choose 4 scoops with repetition allowed, we need to calculate the number of combinations with repetition.

The formula for combinations with repetition is:

\[
\text{Number of combinations} = \binom{n + r - 1}{r}
\]

Where:
- \( n \) is the number of flavors (28 in this case),
- \( r \) is the number of scoops (4 in this case).

Substituting the values:

\[
\text{Number of combinations} = \binom{28 + 4 - 1}{4} = \binom{31}{4}
\]

Now, we calculate \(\binom{31}{4}\):

\[
\binom{31}{4} = \frac{31 \times 30 \times 29 \times 28}{4 \times 3 \times 2 \times 1} = \frac{756,840}{24} = 31,535
\]

So, there are **31,535** possible bowls.

Would you like further details, or do you have any questions?

Here are 5 related questions to consider:
1. What if the bowl contained 5 scoops instead of 4? How many possible bowls would there be?
2. How does the formula change if the order of scoops mattered?
3. What if you were limited to choosing only different flavors, with no repetitions allowed?
4. How many different bowls are possible if you can choose from only 10 flavors?
5. What if the store added an extra flavor, making it 29 flavors in total?

**Tip:** When dealing with combinations where repetition is allowed, always use the formula \(\binom{n + r - 1}{r}\).

Learn how to calculate the number of possible ice cream bowls with four scoops from 28 flavors using combinations with repetition. Understand the formula \( \binom{n + r - 1}{r} \) for combinatorial calculations. Suitable for high school students and anyone interested in combinatorics.

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