# Futher/Add maths product rule for counting

Hi, I don’t understand why I have to divide by 6. Can someone explain it to me please? Thank you.

Question:
A pizza parlour sells 12 different pizza toppings.
Grace orders a pizza with 3 different pizza toppings.
How many different pizzas can Grace order?

12x11x10=1320
1320/6=220

220 different pizzas.

Thank you.
If you don't divide by 6, you'd be saying that, for example, a tomato, cheese and pepperoni pizza is different to a cheese, tomato and pepperoni pizza. Dividing by 6 accounts for the different orders each set of 3 toppings could be chosen, and makes sure you're not counting any combination multiple times.

I don't know what vocab your specification includes, but this is the difference between combinations and permutations if you've discussed them like that
Original post by Interea
If you don't divide by 6, you'd be saying that, for example, a tomato, cheese and pepperoni pizza is different to a cheese, tomato and pepperoni pizza. Dividing by 6 accounts for the different orders each set of 3 toppings could be chosen, and makes sure you're not counting any combination multiple times.

I don't know what vocab your specification includes, but this is the difference between combinations and permutations if you've discussed them like that

Hi, thank you so much for your response! I understand now! Thank you.