Question

You go to dairy queen and are customizing a blizzard. There are 2 types of ice cream, 16 toppings, and 5 syrups to choose from. If your blizzard has 1 ice cream, 1 topping, and 1 syrup how many possible blizzard combinations are there? a 160 b 237 c 87 d 92

Answer 1

Here we do a small diagram just to help us to understand the problem

Let's say that we have 2 types of ice cream (circles), 3 toppings (triangles), and 2 syrups (squares), if we fix the ice cream we have 3 choices of topping, and for each topping, we have 2 syrups, a total of 6 combinations, if we do the same for the other icecream we will have 12 combinations, this smaller problem is the same logic of the bigger problem, in fact, to find the combination we just have to multiply the number of ice creams, the toppings and the syrups.

To see that let's use the same argument, fix the ice cream, we have 16 toppings, and for each topping, we have 5 syrups, a total combination of 80, now -fo the same for the other ice cream we have more 80 combinations, then, the total of combinations will be

`\begin{gathered} \text{ combination = types of ice cream x toppings x syrups} \\ \\ \text{comb}\imaginaryI\text{nat}\imaginaryI\text{on= 2}\cdot\text{16}\cdot\text{5} \\ \\ \text{ combination = }160 \end{gathered}`

We have a total of 160 combinations, the letter A is correct