An ice-cream parlor sells sundaes with 3 different types of ice-cream and 4 different toppings. They have 8 flavors of ice-cream and 10 toppings for their customers to chose from. what is the probability that a customer orders a sundae including the toppings of whipped cream, caramel syrup, chocolate syrup, and cookie crumbles
To calculate the probability of a customer ordering a sundae with specific toppings, we need to find the ratio of the number of favorable outcomes (sundaes with whipped cream, caramel syrup, chocolate syrup, and cookie crumbles) to the number of possible outcomes (all possible sundaes).
First, let's determine the number of ways a customer can choose a sundae with the desired toppings. Since each customer can choose any of the 8 flavors of ice cream, there are 8 choices for the first scoop, 8 choices for the second scoop, and 8 choices for the third scoop. Additionally, there are 10 choices for each of the 4 toppings.
Therefore, the total number of ways a customer can choose a sundae with these specific toppings is:
8 (choices for the first scoop) x 8 (choices for the second scoop) x 8 (choices for the third scoop) x 10 (choices for each topping)
= 8 x 8 x 8 x 10
= 5120
Next, let's determine the total number of possible sundaes a customer can order without any restrictions. Each customer has 8 choices for each of the 3 scoops, resulting in a total of:
8 (choices for the first scoop) x 8 (choices for the second scoop) x 8 (choices for the third scoop)
= 8 x 8 x 8
= 512
Finally, we can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 5120 / 512
Probability = 10
Therefore, the probability that a customer orders a sundae including the toppings of whipped cream, caramel syrup, chocolate syrup, and cookie crumbles is 10, or 10/512.