In how many ways can 14 different pizza toppings be chosen from 15 available toppings?

There are  ways to choose pizza toppings.

To solve this, we are asked how many ways we can choose 14 different pizza toppings from a set of 15 available toppings. This is a combination problem, where the order of selection doesn't matter.

The formula for combinations is:

\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]

Where:
- \(n\) is the total number of items (15 toppings),
- \(r\) is the number of items to choose (14 toppings).

So, we have:

\[
\binom{15}{14} = \frac{15!}{14!(15-14)!} = \frac{15!}{14! \cdot 1!}
\]

This simplifies to:

\[
\binom{15}{14} = \frac{15}{1} = 15
\]

Thus, there are **15 ways** to choose 14 toppings from 15 available toppings.

Would you like more details on this calculation or any clarification?

Here are 5 related questions:
1. How many ways can 13 toppings be chosen from 15 available?
2. What is the number of ways to choose 15 toppings from 15 available?
3. How many ways can we choose 12 toppings from 15 available?
4. How would the answer change if repetition of toppings was allowed?
5. What is the probability of selecting a specific topping in one of the combinations?

**Tip:** For small differences between \(r\) and \(n\), you can often use simple subtraction to calculate combinations directly.

In how many ways can 14 different pizza toppings be chosen from 15 available toppings?

Discover how to solve a combinatorics problem involving choosing 14 pizza toppings from 15 available options. This solution explains the use of the combination formula and the binomial coefficient theorem, making it perfect for high school students (Grades 10-12) learning about counting principles.

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