Answer:
4 is the smallest number of topping available
Explanation:
To determine the smallest number of toppings available, we need to consider the fundamental counting principle.
The fundamental counting principle states that if there are m ways to do one thing and n ways to do another thing, then there are m * n ways to do both things together.
In this case, we want to calculate the total number of different ways to order the pizza with 4 types of pizzas and any combination of different toppings.
Let's assume that there are m different types of pizzas available and n different toppings available.
For each type of pizza, there are n choices for the toppings. Since we have 4 types of pizzas, we can multiply the number of choices for each pizza together using the fundamental counting principle.
Therefore, the total number of ways to order the pizza is m * n * n * n * n = m * n^4.
According to the advertisement, there are almost 16,400 different ways to order the pizza. So, we can set up the equation:
m * n^4 = 16,400
To find the smallest number of toppings available, we can start with a small number of toppings and incrementally increase it until we find a solution.
Let's try different numbers of toppings and calculate the corresponding value of m * n^4:
- For 1 topping: m * 1^4 = m
- For 2 toppings: m * 2^4 = 16 * m
- For 3 toppings: m * 3^4 = 81 * m
- For 4 toppings: m * 4^4 = 256 * m
We can see that for 4 toppings, the value of m * n^4 exceeds 16,400. Therefore, the smallest number of toppings available is 4.
In conclusion, based on the fundamental counting principle and the given information in the advertisement, the smallest number of toppings available is 4.