A dessert menu consists of ice cream or fruit The restaurant

A dessert menu consists of ice cream or fruit. The restaurant offers three flavors of ice cream: vanilla, chocolate, and strawberry. The customer can choose 1, 2, or 3 scoops and can have sprinkles, caramel, or chocolate as a topping or can choose to have no topping. If the customer wants fruit instead they can choose from apple slices, orange slices, mango, or strawberries. And they can be dipped in chocolate or not. If a customer can only pick one dessert, how many possible dessert combinations are there? How many ways are there for three people to order different desserts?

Solution

Number of Possible Combinations = Number of possible combinations of ice-creams + Number of possible combinations of fruits

Ice-cream combinations = 3(flavors strawberry, vanilla and chocolate) * 3 * (1 scoop, 2 scoop or 3 scoop) *4( sprinkles,caramel, chocolate or no topping)

= 3 * 3 * 4 = 36 combinations

Fruit combinations = 4(apple,mango,orange,strawberries) * 2(chocolate or not) = 4 * 2 = 8 ways

Hence total possible desert combinations is equal to

(36 + 8) = 44

Number of ways to order three different people to order three different deserts

= 44(first person can choose any desert) * 43(second person can choose any except the first person\'s dessert) * 42(third people can choose from any of the remaining 42 except the first and second person\'s choice)

=> 44* 43* 42

=> 79464 ways