A small gelateria has ten flavors of ice cream. They also have four toppings: crushed graham crackers, fresh strawberries, jimmies, and whipped cream. How many two-scoop sundaes can be made if the two scoops are different flavors and only one toppig can be selected?
To find the number of different two-scoop sundaes that can be made with different flavors and one topping, we need to multiply the number of options for each choice together.
First, let's determine the number of options for the two scoops. Since there are ten flavors available and we want different flavors for each scoop, we can choose the first scoop in 10 ways and the second scoop in 9 ways (because once the first scoop is chosen, there are only 9 remaining flavors to choose from). So there are 10 * 9 = 90 possible combinations for the two scoops.
Next, we consider the number of options for the topping. There are four toppings available, and we can only choose one. Therefore, there are 4 options for the topping.
To find the total number of two-scoop sundaes, we multiply the number of choices for each component together: 90 (choices for the scoops) * 4 (choices for the topping) = 360.
So there are 360 different two-scoop sundaes that can be made with different flavors and one topping at this gelateria.