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?

Answer:
12x11x10=1320
1320/6=220

220 different pizzas.

Thank you.

Reply 1

Interea

19

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 :smile:

Reply 2

Sasuto

OP

12

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 :smile:

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

Futher/Add maths product rule for counting

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