imagine you are the owner of a pizza shop that offers three different types of crust, seven different toppings, and three different cheeses. How many different combinations of 1 crust, 3 topping, 1 cheese pizza does your shop offer?

Question

anonymous · Answer

Are you familiar with permutations and combinations?

anonymous · Answer

Yes I am. 
That is the topic we are studying right now in math, but I've an answer in two times but my teacher said they were incorrect.

anonymous · Answer

What have you said so far?

anonymous · Answer

Well the first answer I sent in was 252, but I confused myself and put in the wrong equation. 
The second answer was 1260. I used the formula he gave in the example problem but I can't seem to get it.

anonymous · Answer

Using the fundamental counting principle we have 3 choices to multiply together.

# of possible crusts X # of combinations of 3 ingredients X # of possible cheeses

Does that match you analysis so far?

anonymous · Answer

Yes

anonymous · Answer

Since the order the toppings are placed doesn't matter, we use combination

$$C_{3}^{7}$$

so...   3 X combinations X 3

anonymous · Answer

Would it be 3 X 35 X 3?

anonymous · Answer

That is what I got.

anonymous · Answer

So then there would be 315 different combinations