# math

posted by .

I'm having trouble on how to figure something out. The question says a pizza place uses 5 toppings (a,b,c,d,e). How many different combinations can be made with the pizzas having 3 different topping? A

• math -

It's a question about factorials: the answer is the number of ways you can choose 3 from 5. You could enumerate them without too much difficulty, but the shortcut is to work out 5! / (3! x (5-3)!), where N! means N x (N-1) x (N-2) .... x 2 x 1.

• math -

think of it this way:
The pizzamaker would have 5 ways to choose the first topping, then 4 ways to do the second topping and finally 3 ways for the third topping

so isn't that 5x4x3 or 60 ways

• math -

No - you're distinguishing between the 1st, 2nd and 3rd, which you don't need to do. ABC is the same as BCA, which is the same as CAB etc. You've got to allow for all the combinations that are the same.

• math -

David is correct, I was in error

My senior moment of the day.

• math -

In fact, every triple can occur in six different ways - so the answer is actually the 60 you identified, divided by 6.

• math -

I'm in 6th grade and never heard of using ! in math. I guess I'll do it the long way to see how it works. Thanks so much :)

• math -

do 5x3..
its fifteen(:
these ppl are so confusingg;

• math -

Just for the record the answer is ten. They are: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE and CDE.

## Similar Questions

1. ### Intro to probability

A certain pizza restaurant offers three different sizes of pizza and eight different toppings. How many distinct pizzas having two different toppings can be made?
2. ### Math (Data Management)

The student council is ordering pizza for their next meeting. There are 20 council members, 7 of whom are vegetarian. A committee of 3 will order 6 pizzas from a pizza shop that has a special price for large pizzas with up to three …
3. ### math

A pizza place has 5 different toppings. How many different pizzas can be made using a combination of 3 toppings per pizza
4. ### Math

There are six different toppings for pizzas, sausage, hamburger, pepperoni, ham bacon and pork. There are three different cheeses, american, mpzzarella, parmeasan. the pizza comes with two different meats and one chese , how many different …
5. ### Elemements of Math

Little Caesar's Pizza had a commercial on television that claimed you could buy one pizza and get another one free, with up to 5 toppings per pizza (do not count the pizza sauce or the cheese as a topping). The dialogue on the commercial …
6. ### stats

A pizza can be made with any of the following toppings: cheese, pepperoni, sausage, mushrooms, anchovies, green peppers, or olives. How many different three-topping pizzas can be made?
7. ### Finite Math

Pete's Pizzeria offers 30 different pizza toppings. How many 3 topping pizzas are possible (assuming the toppings are distinct)?