13 Ice-cream Flavors You Can Combine
Q. What is the total number of combinations of one ice cream flavor?
I solved the problem by making a visual tree diagram, like the one below. Therefore, a cone with a choice of a flavor and a topping equals 9, and a cup with a choice of an ice cream flavor and a choice of a topping = 9. Since 9 + 9 = 18, there are a total of 18 combinations that you could have.
Q. How many different sundaes are possible?
1 Expert Answer You can do this with each of the 15 ice cream flavors for a total of 15*56=840 combinations of ice cream sundaes.
- Chocolate and vanilla.
- Chocolate fudge and caramel.
- Mocha and vanilla.
- Pistachio and chocolate.
- Blackberry and hazelnut.
- Cheescake and raspberry.
- Coffee and cookie dough.
- Peanut butter and banana.
Q. How many different pizzas can be made with 7 toppings?
In order to determine the total number of different pizzas I can order, when Mama Sid’s offers four toppings, I need to total the entire different one, two, three, and four topping pizza possibilities….
| Number of Toppings | Total Number of Different Pizzas | Differences |
|---|---|---|
| 3 | 7 | 4=2*2=2^2 |
| 4 | 15 | 8=2*2*2=2^3 |
Q. How many different ways can a pizza be made with 4 toppings?
So the total number of 2 toppings pizzas from 5 ingredients is 4 + 3 + 2 + 1 = 10. A similar argument about subtracting from the five 4 toppings pizzas must also produce 10 pizzas. Try it….Extensions.
| Toppings Used | Possible Pizzas | No. of Pizzas |
|---|---|---|
| 1 | Y, G | 2 |
| 2 | YG | 1 |
| Total of pizzas | 4 |
Q. How many pizzas can be made with 3 toppings?
Assuming you get 3 different toppings: The first topping has 12 choices, the second 11, and the third 10 = 12*11*10=1,320. Then, assuming that the order in which you choose the toppings isn’t relevant, we need to remove the ordering of 3 things, which can be done in 3!= 6 ways, so 1320/6=220 possible pizzas.
Q. How many ways can 4 pizza toppings be chosen from 12 available toppings?
Answer: There are 495 different ways to choose 4 pizza toppings from 12.
Q. How many ways can 3 pizza toppings be chosen from 10 available toppings?
/({10 /choose 3} = 120/) pizzas. We must choose (in no particular order) 3 out of the 10 toppings.
Q. How many ways can Patricia choose 4 pizza toppings?
Answer: 70 We count down because each time we can’t reuse whatever topping was picked earlier. There are 1680 permutations.
