Table of Contents
- 1 How many combinations can you make with 15?
- 2 How many choices at topping do you have?
- 3 How many ways can you order a hamburger with 3 toppings if the order of toppings does not matter?
- 4 How many different 3-topping combinations are there?
- 5 How many possible permutations are there with 3 different toppings?
- 6 How many different ways can you put toppings on a pizza?
How many combinations can you make with 15?
Wow that’s 1 Quadrillion.
How many choices at topping do you have?
Counting Combinations
\begin{align*}1^{st}\end{align*} topping | \begin{align*}2^{nd}\end{align*} topping | \begin{align*}3^{rd}\end{align*} topping |
---|---|---|
cheese | pepperoni | olives |
cheese | mushroom | pineapple |
cheese | mushroom | olives |
cheese | pineapple | olives |
How many two pizza toppings can you get from 20 toppings?
You have 8 choices for the first topping. For each of those possible choices, you then have 7 choices for the second topping (since you don’t choose the same topping twice). So that’s 56.
How many ways can you order a hamburger with 3 toppings if the order of toppings does not matter?
A three topping burger has (83) possibilities, or 56 possible burgers. A four topping burger has (84) possibilities, or 70 possible burgers. A five topping burger has (85) possibilities, or 56 possible burgers. A six topping burger has (86) possibilities, or 28 possible burgers.
How many different 3-topping combinations are there?
But they are not different, so we must consider how many different ways to arrange 3 toppings: 3 first toppings. 1 third topping. 3*2*1=6. Divide the possible combinations by the duplicates: 2730/6=455. There are 455 different 3-topping combinations out of 15 different toppings.
How many toppings do you get with 8 toppings?
If you have 8 topping you can first have 0 toppings so thats 1 + 2 of the 8 + 3 of the 8 and so on until you get 8 of the 8. This uses combinations instead of the method described above. So you have the 0 toppings + the combinations of 8 = 1 + 255 = 256.
How many possible permutations are there with 3 different toppings?
This number includes 12 ways with 3 identical toppings+12*11* (3!/2!) = 396 ways with 2 identical and 1 different toppings+1,320 ways with 3 different toppings = 1,728 permutations. If toppings can be repeated and order of placement is not important the number of ways
How many different ways can you put toppings on a pizza?
Makes a difference. A combination of 2 different toppings can be done in 28 different ways. A combination of 3 different toppings can be done in 56 ways. 4 toppings in 70 ways. 5 toppings in 56 ways. 6 toppings in 28 ways. 7 toppings in 8 ways. 8 toppings in 1 way.