A pizza parlor offers a choice of 16 different toppings. How many 3-topping pizzas are possible?
Your answer is

To determine how many different 3-topping pizzas are possible when there are 16 toppings available, we can use combinations. Since the order of the toppings doesn't matter, we use the formula for combinations:

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

where:
- \(n\) is the total number of toppings (16),
- \(r\) is the number of toppings to choose (3).

Substituting the values:

\[
\binom{16}{3} = \frac{16!}{3!(16-3)!} = \frac{16!}{3! \cdot 13!}
\]

This simplifies to:

\[
\binom{16}{3} = \frac{16 \times 15 \times 14}{3 \times 2 \times 1} = \frac{3360}{6} = 560
\]

So, there are **560** different 3-topping pizzas possible.

Would you like more details or have any questions?

Here are some related questions:
1. How many 4-topping pizzas are possible with 16 toppings?
2. How many 3-topping pizzas are possible with 20 toppings?
3. What if the pizza parlor offered 16 toppings, but some toppings can be repeated?
4. How many ways can you choose no toppings (just cheese)?
5. How many 3-topping pizzas can be made if certain toppings are mandatory?

**Tip:** Combinations are useful when the order of selection doesn't matter, while permutations are used when the order does matter.

A pizza parlor offers a choice of 16 different toppings. How many 3-topping pizzas are possible?

Discover how to calculate the number of possible 3-topping pizzas from 16 available toppings using combinatorics. Learn about combinations and the binomial coefficient formula with a step-by-step guide. Suitable for students in Grades 9-10.

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